Be very careful about how you clean amber. Its isn't a precious stone, although we use it for jewelry. Its fossilized pine resin, and it can be very soft.
I wouldn't immerse it soda. Carefully clean the silver bits with a silver cleaning cloth, slightly dampened. When you are not wearing them, keep the earrings in a sealed plastic bag, in the dark. This goes for all silver, as oxygen and sunlight will cause tarnishing. Don't be too harsh with your polishing either...silver is a very soft metal and any designs can be all too easily "polished out"
If you look at large silver items, in museums, they are very often displayed in sealed glass cabinets, filled with nitrogen instead of oxygen, just to stop the tarnishing !
If ever you are in up in Town, please visit the Gilbert Collection in the V+A.
There are wonderful things there, like the priceless collection of snuff boxes.
But they have a smashing collection of silver items, which are well worth visiting.
Hope this has been of some help ...I am a silver fan !