Sticky Trumpet Valves from dirt and rust

Best answer is to get it to an instrument maker/repairer.

However, it's difficult to know what to say without knowing a lot more about the way it was made.

If it has actual iron rust, it is probably steel with plating--the exact metals involved could vary a lot.

Assuming that it is the external valve pieces (not the horn body itself,) there are a a couple of things you could try other than a repair shop.

First, the keys & valves could be sent out to be refinished, including removal of the old plating, polishing and replating the surface.

By yourself, the first thing would be to disassemble the valves and clean them with solvent to remove all the old valve oil--depending upon build up, this may solve the problem, but since you mention rust, I'd assume that the plating is failing too--a situation which will only get worse with time.

You could try the electrochemical process to reverse the oxidation and return the iron to it's original place, check around the net for archaeological artifact restoration., then physically remove the pealing plate at the points of contact.

Overall, the cheapest course is to try cleaning, deal with surface roughness at the contact points, and reassemble and oil it. This might make it functional with minimal aesthetic issues.

A repair shop can restore it to like new--or just to functional....