Smart ways to clean a greasy metal vessel?

The secret to getting meat loaf off is to first soak it in cold water for a good 15 minutes or longer. Cold water soaks are good for high protein food like eggs and meat as well as starches like oatmeal. On a scratch-able surface I like to use a butter knife to gently pry off the material that doesn't wipe off after a soak. Fingernails work too if yours are long enough. Then a gentle rub with a plastic scouring pad, not metal. You just have to keep at it.

This is why I use non-stick, ceramic or glass for meat loaf! It isn't glue, but it's close.

If you want to mechanically dislodge stuff without any scratching, try cleaning it with a silicone spatula, the ones made for baking. They can "lick" a bowl of mousse clean. For something like a meatloaf, a few stray bits will stay, but they should be small enough to get cleaned with a sponge. The large amounts of grease and clumps of protein will be gone. And the spatula will scratch less than a scouring pad, even a plastic one.

For best results, combine it with the soaking GdD suggested. In nonreactive metals, I would suggest adding dishwasher detergent to the soak - it will clean much more than liquid meant for manual dishwashing - but it is not suitable for copper.