The answer is yes, Animate object would work on a corpse. The exact effect would depend on the size of the corpse.

While there are specific defined terms in D&D 5e there are also a equal number of that rely on what the word means in English.

Object - a material thing that can be seen and touched.

Creature - an animal or person.

However there is a caveat. In various effects, powers, and abilities. The D&D 5e rules are consistent in referring to creatures as things that are living or animate. Objects as inanimate things like tables, chairs, rocks, books, feathers, etc. It not spelled out but it is consistent.

The things to remember is that D&D 5e rules are not to function as a wargame. They do not define the boundaries of what is possible during a campaign. The setting is what defines that. Instead they are a tool to aid the referee in adjudicating the action. For example the description of humans don't spell out every detail that could come up. The mechanics about humans are those that the authors feel that are useful or come up often. The important of which is the effect being human on character creation. The author expect referee to use what they know about humans to adjudicate anything that the rules don't cover because it is implied that humans in a D&D setting are just like people in real life only living in that world.

One implication of this is that animate objects doesn't change any other physical property of the object other than to animate with the stats provided. If you were to say animate a block of salt, possible considering what salt miners carved out of their mines, and it was to walk into water, then it is reasonable to rule that it would be affected adversely as salt dissolves in water. Perhaps by treating water as a acid attack on the animated object.

So a corpse animated as a object would still be a corpse and subject to decay, smelling bad, etc. It would not gain the benefits of being undead although at first glance it would be hard pressed for a character to tell the difference. One area where I can see the difference being important is trying to animate a skeleton. It is reasonable to assume that the various create undead spells joins the bones together to form a complete animated skeleton. While a long dead skeleton is merely a pile of separate objects of bone.

For stuff that has no real world analogue, elves, magic, etc. The authors expect the referee to fall back on their knowledge of the fantasy genre. Because the implied assumption that D&D is being used to depict a fantasy setting. Which is why they included a list of inspirational works in Appendix E on page 312.

In fantasy it is tradition for some spells to work on anything, a lightning bolt doesn't care if its target is a person, animal, or a piece of furniture. Some spells to only work on people, for example charming or enchanting a princess. And other spells to work only on objects, like the animated furniture from Fantasia.

RAW - No, Otto's Irresistible Dance is not a Charm spell

It does not say that the target will be "charmed", and the condition it imposes is significantly different than the description of the "Charmed" condition.

OID:

A dancing creature must use all its movement to dance without leaving its space and has disadvantage on Dexterity saving throws and attack rolls. While the target is affected by this spell, other creatures have advantage on attack rolls against it.

Charmed:

A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects. The charmer has advantage on any ability check to interact socially with the creature.

A dancing creature can attack the caster (with disadvantage -- and that disadvantage applies to any attack, not just against the caster) and can cast AoE spells that include the caster and anyone else they choose in the target area with no penalty. They just can't move freely. A charmed character can move freely but can't attack or target the caster.

Furthermore, if it were a Charm spell, it would not be necessary to specify that "[c]reatures that can't be charmed are immune to this spell." That appears to be listed as a special exception.

RAI - No, Otto's Irresistible Dance does not impose the Charmed condition

Jeremy Crawford has tweeted saying:

Being charmed means being subjected to the charmed condition

Since OID does not impose the Charmed condition, the Fey Ancestry resistance to "being charmed" does not apply.

What makes sense?

Webster's dictionary says:

charm: to affect by or as if by magic : compel

Magically forcing someone to dance seems to fall completely within that definition.

I would give those with Fey Ancestry advantage on saves against all enchantment spells that compel the user to do something that is not their own free choice. This includes many spells that do not specifically say they are "charms" or that they impose the "Charmed" condition, such as command, compelled duel, and yes, Otto's irresistible dance. I believe those all fall within the common sense and dictionary definitions of "charmed" in this context, and there's nothing in the description of Fey Ancestry that says it only applies to things that grant the "Charmed" condition.