Is it acceptable to only use refererences from other universities? I am applying to mathematics tenure track positions after a postdoc. I have three research letters from professors at Research 1 universities, and each are AMS fellows. One is my PhD supervisor.

My postdoc department is a midrange mathematics department; its on the rise, but doesn't have a big reputation. My supervisor is only familiar with half of my work, while my other letter writers are familiar with all of my work.

Would it be appropriate to use those three letters from other departments, or would it be a warning sign to search committees if no letters come from my current department?
It is certainly acceptable to not have references from your current institution, but it could raise questions, implying that something went wrong in the current position. Having trustworthy, high-quality researchers, as you've indicated, can overcome this problem, though the question still will remain. 

Your references do not necessarily need to be familiar with all of your work, just enough of it, and more importantly, how you are as a researcher and person. Having a more recent reference letter would give a better description of how you are performing now, in particular, after you left the safety of a PhD position. That is, how you are performing now that you've gone out into the world on your own.

My inclination would be to include a local reference for these reasons.