I have dealt with this problem before with work gloves. For some reason washing them will only partially get rid of the smell. Two pieces of advice I can offer from personal experience are try leaving them out in the sun a few times and let them get really warm/hot. Also try rubbing some baby powder on your hands before you put your gloves on for the day. Usually after a couple of "treatments" you'll notice the smell go away.
Not alot, but enough to stay fresh and unclogged with dirt/salt/skin.
Turn them inside out and put them in the dryer on medium. Dryer heat is good for GTX.
Leather is not meant to be washed in a washing machine, and a dryer will pretty much rape your shit.
make sure they air dry as quickly as possible after every use. do not reuse them when they're wet - have another pair you can take if yesterday's gloves are still damp. just hanging them in a ~70degree room is usually enough.