Is it appropriate to call a research professor by phone or to email one of his postdoctoral assistants if he doesn't reply to emails?
3 of the labs I rotated in were not good fits and another had insufficient funding

Definitely be in contact with your department about this. They need to be aware you're having trouble finding a lab; doing 4 rotations without a home is a concerning circumstance, though I've known people in that same situation that found a lab and did quite well.

a week has passed

A week is almost nothing in academic time, especially for a busy professor and especially around this time of year when for many universities the semester has just ended and people are either finishing up with end-of-semester business (grades, graduations) or perhaps taking some time off after their semester responsibilities have ended.