Yes, "you are welcome to our house" could also mean "you are welcome to have our house", but that would usually be ridiculous in context. I would say "to our house" when welcoming someone at the door. If it were a more general statement I would say "in our house", as in "you are welcome in our house anytime".
So if someone said "Välkommen hem till oss" that would be "welcome to our home" rather than "welcome to our place"? would it also be possible to say "Välkommen till vårt hus"?
Is there any right or wrong on this other than what you would choose to say in a particular situation? i.e. whether you are being formal to welcome people to your place or house or more informal to welcome them to your home? And if you live alone, I presume mig replaces oss?
This comment is related with the syntax, or the grammar of this sentence. I just wanted to point out that this skill was like in a horror movie with a cursed quiz or something: 1)Bakom dig 2)Jag står bakom dig 3)Han kommer före mig 4)Du är välkommen hos oss 5)"Here down everyone floats...", (ok the last one is from a movie :) ). It is bit spooky right? :P