It's Tere not Tera because in "Raaj tere ghar men rahataa hai", the 'men' (and any other postposition- I think that's what they're called- 'in, on, of, towards,' etc.) makes the 'tera ghar' go into the oblique. Ghar, itself, never changes, so here, the tera alone turns into tere.

Raj lives at your house is accepted