TL;DR: We actually don't know much less about the significance of Old Norse mythology in Viking Age society than generally assumed, and the extant mythological texts in medieval Icelandic manuscripts should not be regarded as representative in almost any ways.

Before the discussion, it would be especially useful, or, rather indispensable to check some remarks by /u/Platypuskeeper on the recent changing premises of Old Norse religion in How much do we actually know about the ancient religious traditions, deities and narratives of the Norse?

• Euhemerism in medieval Icelandic texts
• How representative, or useful are the extant Old Norse 'mythological' texts like Poetic Edda to reconstruct the religiosity of the Scandinavians during the Viking Ages?

Such are topics directly concern OP's question above, I suppose.

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The following is just a brief notice on the premises OP mentioned.

1. What role did the deities of Old Norse myth played in Viking Age society? Could 'being human' hinder such a role that people expected the gods to perform?

Aside from the textual evidences in the 13th and 14th century Icelandic manuscripts, we really don't have much contemporary evidences available for pre-Christian Old Norse religion. (Skaldic) poetry and runic inscriptions are almost only two kinds of such contemporary sources from Viking Age Scandinavia, and you might be surprised to know that very few of the latter in fact deal with either Old Norse mythology or pre-Christian religious practices directly. Neither can archaeological sources shed much light on the actual religious practices. Thus, I'll focus on the traces of Óðinn cult in the former category of contemporary sources, praise poems from the 10th century Norway.

 

Put it simply, Óðinn in the 10th century poems was the god of the Norse (male) ruler: his main function suggested in the extant poems was to legitimize the rule of some powerful rulers and his family.

• In St. 2 of Háleygjatal (‘Enumeration of the Háleygir (ruler family of Hálogaland)’), Norwegian Poet Eyvindr skáldaspillir Finnsson narrates the origin of the family of jarl of Lade, de facto the most powerful ruler family in the late 10th century Norway: The ancestor of the jarl come from (ex-marital) one-time affair between God Óðinn and Goddess (or ex-giantess) Skaði. Though the extant stanzas are fragmentary, this poem covers the history of Lade's jarl family from its divine ancestor, Óðinn, to the current ruler, Hákon jarl Sigurðarson (d. 995), by narrating a series of rulers' deed and death. Such Óðinn's role as a progenitor of the ruler family at least presupposes that he could became human's father.
• Old Norse (actually not only Old Norse, but also in some Germanic language) poetry is famous for the frequent use of the literary metaphoric art called kenning, employing improvised compound in place of single word: 'a sword' could be paraphrased as 'the foe of the shield' or something like that. Eyvindr and other skaldic poets who served Jarl Hákon often employs a kenning compound including Óðinn or one of his different monikers to paraphrase the protagonist of their poems as well as the patron, Jarl Hákon. By using this kind of Óðinn-kenning, the poets also tried to project some attribute of Óðinn over their patron, Jarl Hákon, in my understanding.
• Jarl Hákon's dominance over Norway is sometimes represented metaphorically in the poems as a kind of hieros gamos (sacred marriage) between the jarl and the goddess of the earth, or the land of Norway, as Óðinn and some goddesses had: To give an example, the Icelandic poet Hallfreðr vandræðaskáld Óttarsson paraphrases the protagonist Jarl Hákon as 'a commander of the raven gathering place (the battle field)(->warrior= Hákon)', the conquered land as 'wide-headed spouse of Báleyg (= a heiti (moniker) of Óðinn) (->goddess Jörð)' in his Hákonardrápa, St. 8. In a sense, Hákon appears as a kind of avatar of his ancestor god Óðinn, and repeats his deed, such as the marriage with the goddess of the land, in praising poetry. Óðinn was not only a progenitor to legitimize his linage, but also a kind of role model for the rulership for Jarl Hákon.

These evidences are by no means so clear-cut especially for non-speciallists, and some might argue against this hypothesis that these are mere rhetorical-meraphorical expressions in the poems. Nevertheless, it should be underlined here again that these poems are almost only the extant contemporary evidences from pre-Christian Scandinavia during the Viking Age.

 

2. Could a normal human be revered as a kind of the god in pre-Christian Scandinavia?

In fact, there was: The Life of St. Anskar who was comissioned to go preaching in Birka, a town in Sweden in the middle of the 9th century mention that the dead ruler, Erik, was newly added to the 'pantheon' of the gods (Ch. 26). This might be a kind of ancestral cult, but it is worth noting that the Norsemen during the Viking Age did not 'worship' only major deities found in medieval Eddic text. Contemporary poems also mention their practice of offering (blot) to the elves. As I briefly mentioned in this question thread, they even also sometimes didn't hesitate to incorporate Jesus into one of their 'powerful being' list!

 

References:

• Abram, Christopher. Myths of the Pagan North: The Gods of the Norsemen. London: Continuum, 2010.
• Ström, Folke. 'Poetry as an Instrument of Propaganda: Jarl Hákon and his Poets'. In: Ursula Dronke et al. (eds.), Specvlvm Norroenvm: Norse Studies in Memory of Gabriel Turville-Petre, pp. 440-58. Odense: Odense UP, 1981.
• ________. 'Hieros gamos- motivet i Hallfreðr Óttarsons Hákonardrápa och den nordnorska jarlavärdigheten'. Arkiv för nordisk filologi 98 (1983): 67-79.