Consider that the different races where limited to certain classes - or in the case of Skyrim - certain skills and perks.

What kind of classes would you like to bind to what races? You can call the class whatever you like, but skills and perks must match the names of those in the game.

I would also like to read your opinions in what race is lore-wise best suited for what class/skills, and what that same race would be less suited for. I myself am not very learned in the TES-lore.

In my opinion:

Orcs should excel in heavy armor, due to their supposed physical strength. They should also be able to deal very heavy blows either with one-handed or two-handed weapons. The orc would without problems be able to use a shield to deflect heavy blows and, and bash hard with it. The orc could also be a "berserker" with two weapons, preferably swords, and use light armor to gain speed and pure power in his blows. He would be able to kill most threats before they can hit him, thus removing the need for heavy armor. The orc berserker would fight without a helmet so he has full eyesight, and he would want eye contact with his opponent. Orcs would be able to enchance their equipment by smithing and enchanting.

Wood elf would be a very agile hunter, relying on sneak and light armor. He would be able to disptach mosts of the foes with a bow whilst hiding from a safe distance. If they enemy approaches. the wood elf would be able to switfly dance around the target, dodging heavy blows and dealing fast attacks with a dagger. A shield or heavy armor would not suit the wood elf.

This is all I've got time for right now. I'd love to see your opinions.

This is TES.
There aren't any solid "Race=Class" situations.

Exactly. And my question is referring to if that was NOT the case.