I had some reins like that. I soaked them in oil for days -- I would put them in, leave them for the day, at night wipe off the excess, replace or refill the oil, then do it again the next day. Somebody told me to wash them first, but they were so dry I think they would have broken. I just kept that up until I wasn't scared to work with them. Then I let them hang in the air for a while and started oiling them properly. After about a week of this care, they were just fine. I use them all the time now.
I would look after the leather first and then worry about the silver. Silver can be polished later.