Given below is a tabular summary of the ideas conveyed on Angira and His children and some words conveyed at the end of the table below – given my lack of knowledge, I may have made errors in putting this appropriately

Father	Mother	Son	Daughter	Notes
अंगिरा	सुभा	बृहस्पति	देवी भानुमती	Female is अभिमानि देवता of day time
			रागा	अभिमानि देवता of night time.
			सिनीवाली	अमावास्या connected to चतुर्दशी – also known as दृश्यादृश्या, कपर्दिसुता, ‘रूद्रसुता’
			अर्चिष्मती	Connected to the full-moon, referred to as शुद्ध पौर्णमासी
			हविष्मती	First day of lunar fortnight connected to or following पूर्णिमा Also known as राका
			महिष्मती	पूर्णिमा connected to चतुर्दशी – also known as अनुमति
			महामती	One which shines brightly during यज्ञs like सोमयाग, etc
			कुहू	Single कला of चंद्रमा is present via its most सूक्ष्म aspect (शुद्ध अमावस्या)
			भानु	It bears the same स्वरूप as मनु (प्रजापति) who is the son of तपक. The wise ब्राह्मण well versed in the वेद also refer to this भानु as ‘बृहद्भानु’
बृहस्पति	चान्द्रमसी (तारा)	शंयु		First अग्नि into which आहुति of घी is poured into (at the start of दर्श-पौर्णमास)
		निश्ययवन		निश्ययवन’ अग्नि only does स्तुति of पृथ्वी (it is अभिमानी देवता of वाक्) It is निष्पाप, निर्मल, विशुद्ध and always bright.
		विश्वजित्		बुद्धि of the entire विश्व is under its control
		विश्वभुक्		Responsible for digestion of food ब्राह्मणs undertake its पूजा during पाकयज्ञ
		ऊर्ध्वभाक्		Present within प्राणवायु and is a त्रिकालदर्शी Popularly known as ‘उदान’ that moves in upward direction
		स्विष्टकृत्		अग्नि used daily for every गृह्यकर्म; घी poured into it in a northerly direction घी is poured ensures fulfilment of all desires
			स्वाहा	Anger present within all beings
शंयु	सत्या	भरद्वाज	वीरा	सत्या  is always eager to align Herself with Truth (सत्य)
		भरत	Three girls
भरत	Unknown	भरत	भरती	This अग्नि is joyous and since it provides पुष्टि (nourishment), it is also referred to as ‘पुष्टिमति’
		पावक		This अग्नि  was great (worthy of पूजा) and hence given the name of ‘महान्
भरद्वाज	वीरा	वीर		When पूजा of वीर is done, the मन्त्र is pronounced in उपांशु style This अग्नि is given 2nd offering of घी along with सोमदेवता. Also referred to as ‘रथप्रभु’, ‘रथध्वान’ and ‘कुम्भरेता’
		सिद्धि		सिद्धि’ even covered up the effulgence of सूर्य In the आह्वान-मन्त्र, it is this अग्नि named सिद्धि whose स्तुति is done.
निश्ययवन		सत्य		It is निष्पाप and promoter of कालधर्म (also known as निष्कृति) It provides redemption to beings crying out in anguish when suffering from pain. This अग्नि adds beauty/ grandeur to all गृह and gardens inhabited  by the living beings
सत्य		स्वन		This अग्नि is responsible for diseases
विश्वभुक्	गोमती
	स्वाहा	काम		That अग्नि which bears anger within its heart, bears a bow and garland on its body and fights in wars with joy and enthusiasm and destroys enemies is referred to by the name of ‘अमोघ’
		उक्थ		अग्नि whose स्तुति is undertaken in a three-fold manner by the ब्राह्मणs, that अग्नि which created the great sound (परा) and अग्नि that always gives assurance
काश्यप		पाज्चजन्य
वासिष्ठ
प्राणक
च्यवन
त्रिवर्चा
पाज्चजन्य		दक्षिणा
		बृहत्		From the forehead
		रथन्तर साम		From the Face
		रुद्र		From the Navel
		इन्द्र		From the Strength
		वायु & अग्नि		From प्राण
		प्राकृत and वैकृत types of अनुदात्तs, मन & 5 ज्ञानेन्द्रियs (six देवताs) & पञ्चमहाभूत		From the Arms
		प्रणिधि		From अंश of वासिष्ठ बृहद्रथ
		महत्तर		From अंश of काश्यप
		भानु		From अंश of अंगिरस च्यवन
		सौभर		From अंश of वर्च
		अनुदात्त		From अंश of प्राण
		सुभीम, अतिभीम, भीम, भीमबल और अबल		Role of these five विनायकs is to create obstructions and destroy यज्ञs undertaken by the देवताs They abduct the यज्ञसामग्री of people performing the यज्ञ even from स्वर्गलोक. These विनायकs not only snatch away the great offerings meant for (various) अग्निs, but also destroy them. It is because of their proximity to the अग्निs that they snatch away and destroy the offerings.
		सुमित्र, मित्रवान्, मित्रज, मित्रवर्धन & मित्रधर्मा
		सुरप्रवीर, वीर, सुरेश, सुवर्चा & सुरहन्ता
		बृहदुक्थ		When अग्निहोत्र is happening on पृथ्वी, बृहदुक्थ sits in it and his पूजा is undertaken by the best of पुरुषs
		रथन्तर अग्नि		Multiple sons are referred to here and are said to be part of मित्रविन्द देवता
		शिव		Always immersed in doing  आराधना of शक्ति – शिव is responsible for the welfare of all beings who are immersed in दु:ख
		ऊष्मा		It creates heat (ऊष्मा) among all beings
		मनु		It performed the ‘प्राजापत्य’ यज्ञ since it is a प्रजापति
		शम्भु		Resplendent and full of radiance
		आवसथ्य
भानु	सुप्रजा बृहभ्भासा	बलद		भानु here is the son of अंगिरा (also known as मनु) – बृहभ्भासा is the wife of सूर्य. Both of them gave birth to six children. ‘बलद’ is the name of अग्नि that provides strength to beings when they are weak (mother is सुप्रजा)
		मन्युमान्		This is the one which gets expressed as anger within calm beings (mother is सुप्रजा)
		विष्णु’ (also धृतिमान्)		This is the name of अग्नि that is offered in दर्श & पौर्णमास यज्ञ (mother is सुप्रजा)
		आग्रयण		This is the अग्नि whose यज्ञ involves offerring आग्रयण (यज्ञ  that involves offering of new grains) कर्म as हविष्य along with इन्द्र (mother is बृहभ्भासा)
		अग्रह (वैश्वदेव)		The place of origin of eight हविष्य like आग्नेय, etc involved in the चातुर्मास्य यज्ञ – अग्रह is the chief अग्नि named विश्वदेव in the वैश्वदेव पर्व
		स्तुभ
भानु	निशा	अग्नि	रोहिणी	The daugher of मनु is also understood as ‘स्विष्टकृत्’ – Her name is रोहिणी – for some inauspicious कर्म, She became the wife of हिरण्यकशिपु
		सोम
		वैश्वानर		वैश्वानर is the name of अग्नि whose पूजा is done primarily along with पर्जन्य (इंद्र) in the चातुर्मास्य यज्ञ
		विश्वपति		विश्वपति is the name of अग्नि and popularly stated as being lord of the entire जगत् in (the knowledge of) वेद – Owing to its influence, the आहुति-क्रिया gets done in a glorious way by offering हविष्य and this is why it is called by the name of परम स्विष्टकृत् that (one that ensures success of our highest desires)
		सन्निहित		This अग्नि resides in all beings having a physical body and motivates beings to undertake actions
		कपिल		One who is an effulgent महापुरुष, one who is the basis for शुक्ल & कृष्ण movement, one who takes care and feeds अग्नि, one who does not have even a minor blemish or disorder as well as one who is the creator of this जगत् which is continually changing – He is the initiator/ author of सांख्ययोग and He is also the अग्नि named कपिल which acts as a shelter for the fire in the form of anger
		अग्रणी		The अग्नि which is used to offer the first portion of the food before performing all such actions is popularly called as अग्रणी
		शुचि		For errors committed while performing अग्निहोत्र कर्म, मनु has created the effulgent अग्निs for the purpose of undertaking प्रायश्चित्त If the अग्निs comes into contact with each other (accidentally) owing to the influence of wind, then इष्टि (act of आहुति) must be undertaken using अग्नि named शुचि by performing अष्टाकपाल पुरोडाश (this is prepared by keeping the specified वस्तु into eight कपालs and thereby making this sanctified)
		वीति		When दक्षिणा अग्नि comes into contact with two other अग्निs – गार्हपत्य and अहवनीय, one must purify पुरोडाश and keep this in eight vessels and these must be offered into an अग्नि named ‘वीति’.
		वसुमान्		If an अग्नि linked to अग्निहोत्र gets touched by a woman who is in रजस्वला state (under menstruation), then sanctify चरु by keeping it in eight earthern pots and pour this as an offering into an अग्नि named as वसुमान् अग्नि
		सुरभिमान्		If any animal’s dying agony, etc is heard or if any animal like a dog, etc touches the अग्नि (which is part of यज्ञ कर्म), in that state, sanctify पुरोडाश by keeping it in eight earthern pots and pour this as an offering into an अग्नि named as सुरभिमान् to satisfy it.
		अग्निमान्		When अग्नि of a maternity ward (सूतिकागृह) touches the अग्नि of अग्निहोत्र, then sanctify चरु by keeping it in eight earthern pots and pour this as an offering into an अग्नि named as ‘अग्निमान्’ अग्नि
सह	मुदिता	अद्भुत		सह’ is the name of अग्नि that resides in the water- ‘सह’, as the स्वामी of भूलोक and भुवर्लोक, created an अग्नि named ‘अद्भुत’ from her womb. It is accepted by the ब्राह्मणs as part of their वंशपरम्परा that the अग्नि named ‘अद्भुत’ is the Lord of all beings – it is their आत्मा as well as their protector. It is the Lord of all the महाभूत (great elements) of this जगत् – All opulence/ grandeur is situated within it and this illustrious अग्निदेव keeps moving all over at all times. This अग्नि is also referred to as गृहपति whose पूजा is undertaken in various यज्ञ at all times as well as takes all offerings of हविष्य to the देवताs.  अद्भुत अग्नि is one that purifies this entire जगत्. This अग्नि is also responsible for various types of धातु, sulphur, तैजस type of minerals, देवदारु (Deodar) trees, crystals (स्फटिक),E80 emeralds (मरकतमणि), Wood, stone, iron, clouds & corals
				सिन्धुनद, पंचनद, देविका, सरस्वती, गंगा, शतकुम्भा, सरयू, गण्डकी, चर्मण्वती, मही, मेध्या, मेधातिथि, ताम्रवती, वेत्रवती, कौशिकी, तमसा, नर्मदा, गोदावरी, वेणा, उपवेणा, भीमा, वडवा, भारती, सुप्रयोगा, कावेरी, मुर्मुरा, तुंगवेणा, कृष्णवेणा, कपिला and शोणभद्र — all these are नदी (river moving from East to West) and नद (river moving from West to East), and are understood as the place of birth of various अग्निs.
		आप		This अग्नि is a महाभाग (has great fortune), enjoyer of सत्त्व, protector of भूलोक and Lord of भुवर्लोक – that great अग्नि named अद्भुत is seen as the अधिपति of बुद्धितत्त्व (at ब्रह्माण्ड level, this is referred to as महत्)
अद्भुत		भरत (नियत)		it is the one which cremates the bodies of all beings – भरत is always present at the अग्निष्टोम यज्ञ and for this reason, it is also referred to as ‘नियत’ – the संकल्प of नियत is the highest (best)
		विभूरसि		The number of  अग्निs mentioned is the same as that of सोमयागs. All these अग्निs were born as progeny in the वंश of अत्रि, the mind-born son of ब्रह्मा – When अत्रि desired to create living beings, He held those अग्निs within His हृदय – then various अग्निs emerged from the body of that ब्रह्मर्षि

As a lay साधक, I will certainly need help of experts who can help elucidate what is going on here. Within the महाभारत, this is certainly a mystical expression of वैदिक wisdom. From my tiny brain, some superficial observations are given here:

1. It is clear that अग्नि is significant for वैदिक धर्म – in fact, ऋग्वेद begins with a praise of अग्नि.
2. अग्नि is seen as the source of life as well as expression of life. If अग्नि is understood as heat, all life and all expressions of life may be seen as modification of अग्नि in some form or another.
3. अग्नि may thus be seen here as the primary principle of life and children of अग्नि may thus mean emanations, qualities or cosmic forces that proceed from a primary principle.
4. When “sons” are indicated, the son’s (like बृहस्पति) represent active, projective forces of light and knowledge.  बृहस्पति is often expressed as the intellect of the देवताs. “Daughters”, on the other hand, may be identified with lunar phases and more subtle cosmic rhythms which are receptive, cyclical and connected to time & fertility.    
5. अंगिरा may thus represent the primordial fire of चैतन्य that generates both discriminative wisdom and rhythmic/ cyclical awareness and thus mirrors the human minds in two modes – विवेक (discerning wisdom) & अनुभव (experience).
6. Much of the सहस्रनाम literature contain words that are given here – since अग्नि is a primary ingredient within the entire process of यज्ञ, the external conduct of यज्ञ is thus an outer representation of inner forces of यज्ञ that govern life and activity.
7. Sri Aurobindo in this book “The Secret of the वेद” reads the अंगिराs as representing the inner faculties of the humans that seek and find the hidden light – the “finder-seers” recover the Sun hidden in darkness with progeny being various powers and faculties that participate in this inner quest.
8. There is a specific wisdom I have come across which states that when we see the lineage descend from अंगिरा to बृहस्पति to स्वाहा to उक्थ to पाञ्चजन्य, we are watching the sacred fire becoming more and more specific – from the primordial luminosity of अंगिरा to wisdom of बृहस्पति to स्वाहा as the देवी of oblation (whose very name is exclamation of the fire offering) to उक्थ (which means recitation or a स्तुति) and finally to पाञ्चजन्य which is the five-fold fire born of the recited word. And thereby, the children of पाञ्चजन्य represent the specific blessings, powers and cosmic functions that flow when all these elements are properly aligned in the यज्ञ
9. There is another explanation I have come across – that पाञ्चजन्य’s chidren represent the five-fold powers of inner awakened fire within a living being – प्राण (breath), चक्षु (vision), श्रोत्र (hearing), मनस् (mind) and वाक् (speech). And when these are properly cultivated through the process of यज्ञ, they give birth to further refinements which are referred to as descendents of पाञ्चजन्य.
10. From a simple reading of various पुराण, अग्नि is often seen as associated with रुद्र, नृसिंह, हनुमान, सूर्य and above all, कार्तिकेय. In fact, within the महाभारत, the story of कार्तिकेय comes immediately after a thorough description of the story of अंगिरा

Now that my own infantile prattle is done with, I will certainly be grateful if some wise person can lead me to the source and meaning of the entire narrative of अंगिरा as conveyed by मार्कण्डेय to युधिष्ठिर.