Due to the smell, I'm having to do my boiling in the garage. Can I mash inside and just carry the mlt out to the garage when I'm ready to sparge and boil, or will moving the MLT around result in stuck sparges?
I've mashed inside on cold days before. If you have the means, I recommend doing the sparge indoors as well, then carrying the full kettle out to the garage for the boil.
No issue in that, just do it all one place or the other or you will have to do extra vorlauf's to re-establish your grain bed.
Also, I wouldn't worry too much about doing it all in the garage, many of us do that. I like the convenience of having my boil burner and my MLT near each other so that the runnings can be heating between batch sparges.