"Raj eats in this room."
Translation:इस कमरे में राज खाता है।
The object of the postposition में is the noun phrase 'इस कमरे'. So, both इस and कमरे are in the oblique case.
Just for fun, you can also have a sentence like राज इस घर के एक कमरे में खाता है। (Raj eats in a room of this house). The object of में is the whole phrase 'इस घर के एक कमरे' and all the words here must be in the oblique case. This is why के has been used instead of का.
To address some of the questions/comments here: "Raj eats in this room" can be the correct answer to 2 questions, but the answers change in Hindi depending on the wording (both should be accepted): Who eats in this room? Since 'this room' is the given in the question, the answer should have the room first: इस कमरे में राज खाता है। And for "In which room does Raj eat?" राज इस कमरे में खाता है would be the better answer.
You are right. When we say a word is in the oblique case, it is the object of a postposition (Hindi uses postpositions rather than prepositions like English). When this happens, the word is used in a slightly different form (like kamre instead of kamra).