Guessing that they're gold with various stones, I would see how far you get with a toothbrush and ordinary hand soap as most of any dirt will be just normal grot.
Some semi precious stones, pastes etc can be damaged by chemicals so avoid it unless you know what you've got.
i agree with brucie - would suggest filling a basin with warm water and some washing up liquid and leave jewellery in it for a short time, half hour would do it and gently polish with a soft cloth.
I have put my platinum and diamond rings in the dishwasher before. Also, when my mums cousin once came over from Italy, he was a jeweller, from a whole family of jewellers, and he put my mums jewellery in a pan and boiled them. They were fine!
Yes, I put my rings ,bracelets, necklaces all in a small pan & bring them to the boil & boil for a couple of minutes, you can see the dirt & muck float off.
Brush with a toothbrush and Colgate toothpaste. My brother shared this tip with me and it really does work. At first I thought he was joking but I did give it a try and to my surprise it did work!