It’s been awhile since I attempted to do a … relatively succinct ‘synopsis’ run-through of Shiva, Odin comparanda (viz. the Indo-European Sky Father deific complex); and so, most of my reply to this gentleman’s good-natured inquiry upon the subject.

I really should actually sit down and i) more actively integrate the Zeus / Jupiter elements (some are mentioned herein, most others are not); ii) expand upon some points; iii) add in a few further points viz. Rudra & Odin specifically; iv) make things easier to follow via properly ‘mapping’ some of the myths (and other features) involved on a direct side-by-side basis.

So – definitely not ‘complete’. But it’s a start.

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Rudra is, as with Odin, an expression of the Indo-European Sky Father deific complex [ref. ‘Dyaus Pitar’ – Zeus Pater, Jupiter, etc.]

The ‘One Eyed’ point – we would observe Ekadrish/Ekadrishti, Ekanetra, and Ekaksha … all theonymics one encounters in the direction of Shiva/Bhairava.

Although to speak more generally – two of Rudra’s Three Eyes, the Moon and the Sun, one generally only sees ‘One At A Time’ up there in the Sky.

To speak toward nomenclature – one observes that both Rudra and Odin are ‘two-faced’, so to speak. That is to say there is a ‘Positive’ and a ‘Wrathful’/Furious’ visage in each case. Something interestingly also observable viz. Zeus Maimaktes (‘The Raging/The Stormy/The Furious’) relative to Zeus Meilichios (‘The Approachable/The Propitiable/’Zeus-Be-Nice-Now’ per one gentleman’s translation – ‘Shiva’, indeed; the literal meaning for ‘Meilichios’ working out around ‘Sweet[ened]’).

In the case of Odin this concept is ‘Tveggi’ [ref. Völuspá 63, Óðins nǫfn 8]; and is directly extolled in the Ynglinga Saga, which features Him ‘changing form’ (“skipti litum ok líkjum”) between the two ‘Facings’, and with the rather useful ‘Grimmligr’ with reference to the more ‘Furious’ facing.

To quote my own translation for TS V 7 3 upon the subject viz. Rudra:

“Verily, Rudra, Who this Living Fire [Agni] Is
Of Variegated Radiances, He –
The Terrific ‘Ghorā’, One ;
the Other, The Beneficent Śivā be.
Through ‘Śatarudrīyam’ Feeding-Flames,
This ‘Ghora’ Form They Appease ;
Whilst with ‘Vasordhāra’ nourishment,
That ‘Śiva’ Face They Please.”

One would also observe that as applies the ‘core’ theonymics – Odin connotes just such a ‘Furor’ situation … ref. Ugra, etc.

As applies “Asura” … you are mixing up two very different terms. For simplicity I tend to prefer to utilize “A’Sura” for the demonic variety – it conveys the “Opposite/Opposed to Sura” more usefully.

You shall find that as applies “Asura” as in “Mighty” … is encountered a number of times in the RV in direct relation to Rudra [c.f. for instance RV II 1 6 – which handily also identifies Rudra with Dyaus, because that might also have come up as a query. And, for that matter, RV VIII 20 17].

This has nothing to do with the later prominence for the term “A’Sura” in relation to, well, demons opposed to Gods. And, in fact, the archaic “Asura” is utilized not only in relation to Gods, but even powerful humans in the RV (see my work “Asura Aesir A’Sura” for more details)

Now, what should also be observed is that the designations for ‘God’, ‘The Gods’ … the ‘standard’ one is most definitely in-use for Odin and the Gods in Nordic perception – ‘-Tyr’ (singular) as in ‘Hertyr’, ‘Sigtyr’, etc., the ‘-Tyr’ cognate with ‘Deva’, ‘Deus’, etc.; and also in plural/collective: ‘Tivar’.

In terms of various points in relation to a more direct demonstration of similarity … we would note that both Rudra and Odin are associated with Crows/Ravens (ref. AV-S XI 2 2), Wolves (and, in particular, Two Wolves … Sankhayana Srauta Sutra IV 20 esp.), wielding of a Spear (‘GeirTyr’ and ‘ShulaPani’, indeed), show up in relation to the Divine Rite of the Covenant (Tanunaptra / Sætt , in Sanskrit & Old Norse, respectively), both are patrilineal to the Horse Twins (Asvins / Divo Napatah, Hengist & Horsa respectively – ref. the Dioscuri / Dioskouri in Roman/Greek terms), both also have the strongly coterminous ‘female retinue’ viz. Rudraganikas (detailed at several points in AV-S XI 2 – line 31, line 11, and elsewhere in the canon; and most interesting in relation to the ‘sidereal’ expression, also) … that map directly viz. Valkyries [including the, again, ‘sidereal’ expression as human women – as seems to have been the case with the ‘reincarnating’ instance(s) with relation to Helgi Haddingjaskati/Helgi Hundingsbane … Kára/Sváfa(Sváva)/Sigrun/Brynhildr etc. … you may also b e familiar with Sundarar & Paravai]; and as I had noted, the ‘Wild Hunt’ situation co-expresses viz. the Ganas of Rudra (esp. the BhutaGana, for the ‘Ghostly’ element), and the Einherjar etc. – as well as, of course, ‘folklorically’, the ‘actual’ Wild Hunt as applies Odin (or His Wife); speaking of His Wife – consider the situation viz. Kali in relation to Skaði (although this is … a whole other extended commentary).

and we may even observe some directly coterminous mythic occurrences – the situation viz. Odin in the Ynglinga Saga and the opening up of the hills/earth to recover stolen wealth of cows mapping directly onto Brihaspati’s deed (given both are accomplished via the utilization of ‘priestly’ means of invocation etc.), Brihaspati being Rudra per Tait. Aran. I 10 1, and most readily observed when considering the situation around Tisya/Pusya (the former being directly a Rudra theonymic, whilst also being name for Pushya nakshatra … and the relation of this esp. viz. Paosa & ‘Tishtrya’ in Iranic, to what in the West we would know as ‘Sirius’; in any case, observe the coterminity of meaning for Pushya and Ardra);

the situation aforementioned viz. Tanunaptra / Sætt – which, conveniently, comes with its own mythic contextualization in each case (in the latter case – contra Ymir; in the former case, Rudra);

the situation with regard to the ‘blue neck’ – which, in both cases, revolves around an imbibing and a (seeming-)death-risk, proximate to yon Axis Mundi; the Samudra Manthan occurrence having had the Mountain utilized for the churn of the Sea of Milk, the Germanic one featuring Yggdrasil.

the results in the former case? Amrit (well, after Halahala); the latter? Well, Runes – but there is also mention made for Kvasir (‘That Which Is Pressed’ – ref. ‘Soma’) in a suspiciously similar context. And the utilization for Amrit/Soma in similar fashion to the Mead of Poetry (Kvasir) – well, again, the parallel is both there and quite logical ; esp. in light of Sigdrifumal 13-14 (which happens, rather interestingly, to map fairly ‘directly’ upon the concept of a Tantrika initiation – the mortal hero in the position of Odin / Bhairava, the Valkyrie as Freyja / Devi).

The results of this ? A blue-neck – some tellings have it in Rudra’s case due to Parvati’s Hands and a strangulation to prevent the Halahala from going down any further. In Odin’s case … well, hanging; and perhaps this aids in explaining His ‘Blue Hood’ about the neck. Perhaps one might consider Vasuki as the ‘Rope’ of the Churning, about Rudra’s Neck, in similar relation to a Hangman’s Noose. Perhaps not.

And, speaking toward Soma / the Mead of Poetry – we would note the situation viz. Rudra/Agni in Falcon Form bringing such, the connexion with 3 vessels and 1 portion that is dropped; exactly as Odin brings in Eagle Form the Mead of Poetry, 3 vessels, with one that is dropped.

We would also note with interest some direct parallels in worship / propitiation – the Tryambakah Rite and the Crossroads, with this showing up even well-post Christianization in the court-records of Sweden (because the people undertaking such were being prosecuted for doing so …), etc.

There is quite a lot more which I could say about all of this … but that should be enough to get you started.

I thought this might be a more fruitful approach than simply posting half a dozen (or half a hundred) links to my previous work and being like “Read These.”