Q:

Do Odin and Thor eat and drink?

Do Marvel's Thor and Odin require food and drink (human food and drink) for their energy, or no? Is this shown anywhere in canon sources?

A:

Yes, the Asgardians can eat and drink. They do so with great relish and enthusiasm. Do they NEED to eat and drink? A completely different question. The Asgardians of the canon Marvel Universe, do not appear to utilize food as their primary source of personal energy. Thor has gone for very long periods (months) in space without eating and did not seem to weaken or lose his fighting prowess.

The Asgardians may not need to consume food to live, their immortality and superhuman vitality comes from the Apples of Idunn, which as long as they consume them on some as yet undisclosed time period, they maintain their youth, vigor, extraordinary regeneration, durability and superhuman abilities. 

"The Gods gained their wisdom and youth and vigor and verve from these apples. Everything that made the gods godly came from these golden fruits only the enchantress could retrieve."

The Apples of Idunn must be consumed regularly or the Asgardians will lose their godly vitality and near-immortality.

Thor : Age of Thunder (2008)

Given the Asgardian molecular makeup (their molecular makeup is three times denser than normal humans) it is unlikely normal human food is able to even nourish them in any significant way. There is no reference to Asgardian foods being more substantial or offering greater than normal benefits.
However, Asgardians in the Marvel Universe appear to enjoy their physical bodies and relish the opportunity to eat and drink, so it is safe to assume Asgardians eat because they like it, not because they need it. When Loki was imprisoned for betraying Odin and Asgard, he did not eat while chained below the Earth. While Asgardians resemble humans, they are NOT and Marvel has indicated they are aliens who have taken Human form, thousands of years ago.

This image denotes Marvel's official position on the Asgardians as aliens. From Thor #493 (written by Warren Ellis and Mike Deodato)
Things to be remembered about Marvel's Asgardians:

Marvel's Asgardians were based on the deities of Norse myths of old. But they are not those deities.
They are an advanced species of humanoids who resemble humans and have technologies so advanced they appear as magic to humans.
They are extremely long-lived as a species and have superhuman levels of strength, vigor and physical vitality. As such, myths may not take into account the actual capabilities of these beings.
While they consume the Golden Apples of Idunn, the actual mechanics of how those Apples work have not been defined in the comics, only expressed in myths and legends.
Most Asgardians expected to survive until Ragnarok, with the occasional death of lesser gods at the hands of their powerful enemies such as the Frost Giants or Fire Giants.

A:

Thor is shown eating and drinking on a pretty regular basis in both the comics and film canon. Invariably we see him consuming heroic (pardon the pun) amounts of both food and drink.
Cataclysm: Ultimate Spider-Man #1

Thor: God of Thunder #13

Movie : The Avengers

Movie : Thor

We also see Odin drinking (with a bear):
Ultimates vol 5 #1

and of course, both of them enjoy Twinkie bars (who doesn't?)

