All possible permutations of on/in/at, in both slots, are grammatical English sentences, but one choice ("in" for both) is the convention in my dialect. I'm just going to discuss the part about the television; the logic is the same for the sofa set.
The central meaning of "in" is "inside": A gift is in a box. For a noun to be in a corner, therefore, you should be talking about the concave side of the corner. This is normally how we talk about the corner of a room in my dialect, so "in" is the natural choice for me for both the television and the sofa set. In might also be how we talk about the corner of a building: The manager's office is in the northeast corner of building 12. However, we might be talking about the outside of the building, and then you would use at instead: There is an oak tree at the northeast corner of building 12.
The central meaning of "on" is "stacked on top of". It is difficult to imagine a situation where something could be stacked on top of the corner of a room, so "on" sounds very strange when you are talking about the position of objects within rooms. But you would say that a dinner plate is on the corner of a table. On is also used by convention when describing where buildings are relative to streets: Building 12 is on the corner of Route 19 and Tower Road. This is perhaps because the building is, if only metaphorically, stacked on the ground at that location.
The central meaning of "at" is "located at a definite point in space". It is not wrong to use "at the corner" for all of the above examples, but when a more specific spatial relationship applies (insideness, stacked-atop-ness, etc) English prefers that you use the more specific preposition.
The television and sofa set being inanimate objects is not important. I cannot presently think of any preposition that cares whether the noun is animate.
Regarding one teacher saying that on should be used for a television relative to a corner of a room, I find that peculiar, but I can make up a motivation for saying it that way. Normally you would not put a television directly on the floor; there would be a piece of furniture (a table, let's say) to raise the TV to a comfortable viewing height. I would describe this situation as: the TV is on the table, but both the TV and the table are in the corner. Your teacher may instead feel that only the table is in the corner, and because the TV is on the table it is also on the corner. I would not be surprised to learn that this is a difference of dialect.