With a few caveats, you can compost canned tomatoes. The bacteria that can spoil canned goods are anaerobic, so once exposed to the air, they will start to die. You want to make sure that you compost pile is "working" (hot enough), so that once you throw the tomatoes in there, they will start to breakdown quickly. I would bury them and make sure that animals or kids can't get into it and wash up really well when you're done. If your city collects compost, the tomatoes can go in there. 

Should I treat those jars in any particular manner before using them again? I'm going to clean them in the dishwasher, but it looks like that goes up only to 140 degrees F. 

That's a bit beyond my purview as a master gardener, I can't safely answer that question for you.

You might be able to find the answer you're looking for here: https://www.extension.umn.edu/food/food-safety/preserving/ or here: http://nchfp.uga.edu/publications/publications_usda.html