What to do with dead birds?

Just leave them for food for other animals to go thru winter time.
It’s called natural selection. Weak individual has to die so the strongest genus can be passed ( not always applies to human ).

You are right. I'll take them to the forest. I thought it would be a shame to leave them to rot, but I forgot that they can help other animals get much needed food. Thank you!

I am always ask where I dump/despose of all the excess or unwanted specimens/insects in my traps.

I have Bait Traps out all winter. Whenever I empty my traps I have a spot near by where I dump out the old bait. I can leave hundreds of unwanted specimens from a light trap at a dump site. When I return the next time to check my trap, absolutely every single specimen or insect will be gone.

While living in Kentucky I had a spot in the forest where I dumped the unwanted specimens from my Light Traps. When I return the next day, the unwanted insects are gone. Every single one.

When I checked my Bait Traps in the forest, I would dump the unwanted specimens on a piece old lumber ten inches by sixteen inches. When I returned, even just an hour later, everything I left was gone.

bad jokes? you must have missed my comment about hedgehogs vs beavers in the "early spring" topic.

You should contact a local or regional natural history museum. They likely have salvage permits to take animals like this, and if they want the specimens they will instruct you on what to do. Usually that's bagging them in a ziplock with the location, time, date, etc. and storing in your freezer until you can drop them off.

Or you could capture some data from the poor animals by taking photographs and uploading to iNaturalist, and then leaving for nature to take over. It would be interesting to document the impact it's having on bird (and other) populations!

I once found dead hummingbird. It flew to the large window and broke its neck. When I tried to open it to remove organs in order to dry and fill up with cotton I ruined it.

I wouldn't joke about that, what's goofy today.. 

I always feel bad for the birds that smack into our windows, sometimes, it's a clean kill, other times, just a thud and  feathers.

A few times I've had a tweety bird peck at the window, like some Hitchockian avian, I still feed them, though, what you don't want to
do is leave anything like a fast food bag lying in sight of the crows, one time at lunch, I looked away and one had my cheeseburger. 

Hummingbird in the house! I had an uncle that teased my little sister at the time, they always go for the eyes.