The table is in the corner of the room. The table is at the corner of the walls. Both are correct when used like this: .... in the corner (of the room). .... at the corner (of two walls).

When using table it is most likely IN i.e., the table IN the corner of the room. But you would say the table AT the corner of the street (thought I can't think why anyone would ever say that) Better example The man in the corner of the room The man as the corner of the street.

What TbilisiTime answered above. It could be used both ways, as well, if you think of a large room where tables are set up in one section of it, with a table in the corner of the room, and a table at the corner of the section (which may be in the center of the room, but is the corner table of the section).