I need to send a package in one of those priority "if it fits it ships boxes" when the post office won't be open. Do they have the boxes for that in the self serve lobby, and do they have a kiosk where I can weigh it, get the postage, etc?

The main post office on Pine street , University place post office, and Lakewood post office have a 24hr lobby with boxes and kiosks for your needs.

Yep, what he said

So i noticed this post office opens 24hours. The little machine right when you walk in. It does absolutly Everything! sends all priorty flat rate, non flat rate and first class it even sells stamps, prepaid package reciept and does P.O Box payments. You can do certified and insurance as well. As a matter of fact I'm standing right in front of it as we speak. Only thing you cannot do is send international.