puppy urine smells like urine. if you've ever smelled any kind of urine in your life, you know what it smells like.
i suggest buying some nature's miracle. this will break down urine, feces, drool, and basically anything else that comes out of a dog's body. even if the toy is just covered in drool, it still needs to be cleaned.
Cutting the grass if it's long is a good idea; it's possible he ran into a snake out there. You should check him for any bite marks, just to be safe. Even if he wasn't bitten, a sudden encounter with a snake (or a rat, or opossum, or any other critter he's not used to) could have spooked him.
As for getting him used to the yard again, I think your idea of using treats is a good one, especially if your dog is particularly food-driven. (Just make sure you don't leave any bits of cheese or hot dog out in the yard when you go back in, so as not to attract other animals).
Are there any toys your dog likes to play with inside? Try taking them outside and engaging with him in play out there. Give him lots of praise any time he runs after a treat or engages in play in the grass.
Until he gets used to being back in your yard, I'd take him on as many walks as possible. Since dogs love to pee on spots where other dogs have peed, it should get him used to peeing on grass again. If you're gone for several hours at a stretch, walk him before you go, put him in a crate with some toys or things to chew on before you leave, then walk him again as soon as you get back. (If he's not already crate-trained, just google "crate training" - most dogs actually feel safe when they're in a crate, as long as you make it comfortable for them by providing a towel to lie on and some toys.)
Finally, for any accidents that occur inside, I've always had a lot of luck with Nature's Miracle.
Best of luck to both of you!
I don't have any home remedies if that's what you are asking for....
But here are some products that I use. Steam cleaning several times is probably a good idea, in addition to using some (or all) of these. I'd imagine if the scent is sticking around, it's probably soaked into the pad or even the wood underneath :(.
My MIL has used This to soak clothing that has had cat pee on it. When my cat was having issues in the house, we used this also. It's pretty good, but you have to really saturate the area, so there's drying time involved.
I use This on a regular basis for cleaning up everyday messes.
I use This when I vacuum. I suppose you could use plain baking soda?
I would also recommend wiping down the desk and walls and baseboards in case the scent has permeated those also.
Good luck, and I hope you get to move back to your place soon!