Beautiful stones, first of all. What a find!
You can cleanse with sunlight, for a little while. It can bleach out stones like amethyst so I wouldn’t do it too much. Full moonlight is a great way to cleanse your stones and a lot of people do that.
Selenite is a natural cleanser, it’ll charge your crystals for you. I have a little selenite disk I put my crystals on and that helps.
As @Liisa said you can bury your crystals in a pot of plants or by a tree and let the earth cleanse them. That’s a good option.
Personally, I just to smoke cleanse mine. I use a palo santo stick on it and cleanse it that way.
I would not use water, some crystals react to water and dissolve a bit in it, like selenite, so there’s that. But any of the other three elements can be used to cleanse.
Anyhow, hope this helps. I’m not an expert on crystals so hopefully one of our crystal mavens will have more information for you.