Learn Croatian: Oni imaju doručak, ali žele ručak. - They have breakfast, but they want lunch.

Yes, they are the direct objects, so they are in the accusative case. However, for masculine nouns that represent non-living things (inanimate objects) like doručak (breakfast) and ručak (lunch), the accusative form is exactly the same as the dictionary form. You don't need to change the endings at all!

Both imaju (they have) and žele (they want) are used for 'they', but one ends in -ju and the other in -e. Why?

Croatian verbs fall into a few different groups based on their endings. Imati (to have) belongs to a group that uses -ju for the 'they' form, making imaju. Željeti (to want) belongs to a different group that uses -e, making žele. You will slowly learn these patterns as you meet more verbs.

Could I just say Imaju doručak, ali žele ručak without Oni?

Yes, absolutely! Because the verb endings (-ju and -e) already tell us that the subject is 'they', the word Oni is completely optional. Native speakers usually drop it unless they want to put special emphasis on who is doing the action.

I don't see words for 'a' or 'the' before the meals. Is that normal?