My sea strainers are dripping into bilge. Is there anything I can do while the boat is in the Water

if you dont have ball valve before strainer... no!
or you can try it by blocking the hose with a rag but that is a more risky way to do it!

Most of the time, there should be a ball valve between the pickup and the sea strainer. Else, what good is the SS if you can't stop and open it up to clean it?

Close them off, and open them up. Depending on which SS you have, you may have a cracked lid, or a bad seal/o-ring that might need replaced. Pics would help.

Not sure if this photo displays it or not but sea water is coming in and dripping off the bottom of them

damn...looks like more than a 'drip' to me! And yeah..I guess I always thought one could close an up-stream valve and shut off the water so one could clean them as necessary, at sea. Guess I have been wrong all these years.

That green shiit on there is bad. You have a leaky ground somewhere and the bottom is probably corroded.

Have same exact strainers in shed! I removed them because kept dropping wing nuts in bilge on old boat Glass or bottom seal cracked just a guess?Good luck merry x mas

Is that a pic from The Titanic?