Please understand that I first and foremost want your marriage to work out, and it was from that place in my heart that I still wrote the following:
You could get a cheap GPS tracker, or track his cell phone (easy to do through your provider's website). But there are other ways to know.
I think the fact that he won't tell you where he's living is nearly admission. He seems to be shielding someone else, and perhaps himself.
I don't want to tell you what to do, especially since I don't know the full of your situation. I know that based on what little I do know, in your shoes I would get a pit bull of a lawyer, make serious perpetration for damage control (open separate bank account, transfer funds big time so that he can't clean you out, pick and choose what you can do without, send a few important items like birth certificates, car titles, and any heirlooms to your Mom's for safe keeping, etc.), and change the locks.
If you have certain models of Kwikset brand locks, you may be able to do this at home yourself. If you don't have that model, but do have this brand (and some other brands as well, a simple phone call can verify this locally), the major chains of Big Box home improvement centers (The orange guys, the blue guys with the red stripe, likely others) will reset those locks for free as long as you have a key that you want it changed to. (I've heard of people re-keying their house to be the same as their mom's so that she can come help with the kids.) If you know how to operate a screwdriver, you can remove and re-install the locks yourself. You might mark them with a little tape to put them back in the same spots so that it LOOKS like nothing changed. You can then have a good friend run them to the store for you, or sit at the house while you're gone with the locks. I'd bet money that there is someone at your church whom you could trust in this moment to help you.
From the moment that my ex filed divorce papers, I wouldn't let her back in the house, traded her my key to her car for her key to my car, and started keeping things locked that I had previously left unlocked. I live in a good neighborhood and didn't lock my car...until then. I've heard of some deviousness and didn't want her to have the opportunity to plant something then make accusations. She had fallen into a crowd of people before who gave her access to illegal drugs. I'd been clean for more than a decade when she left me, but I knew that it would seem credible if she was able to get drug charges on me as a ploy to get the kids, or anything else she might want in the divorce. I'm not saying to do this. I am saying protect yourself from the possibility of someone doing it to you.
Thinking about your opponent's next move is good in checkers. Thinking about your opponents next several moves is winning chess. Divorce is no game, and should only be entered into when absolutely necessary. If this is even a possibility, it may be wise to plan for what you want out of it so that you will know how to get there before someone is there first. Maybe you can still get back together, but if you are already to the point of thinking about having to provide for yourself (looking for work, you said) then it may be time to prepare a solid exit strategy just in case.