Is it possible to move all my groups to a new Yahoo ID?

The group you own is easy. Join it, use the old screen name to make your new one the owner. Than go to the place under the new one and delete your old screen name from the members list. As for the other ones it helps if you have friends on them that now about your new screen name. They can delete to old one and invite your me one to jion up.

There is no way to automatically change your Yahoo ID in a Group. You're going to have to subscribe to all your Groups under your new Yahoo ID (though you don't have to also unsubscribe from all your Groups under the old Yahoo ID if you don't want to). And for the Group you own, after you join it as an ordinary member under your new Yahoo ID, you have to go through the extra step of logging in to your old Yahoo ID and going to that Group to make your new Yahoo ID a co-owner of the Group. To do that, click Members on the left-hand side of the Group's web page when logged in as your old Yahoo ID. Then locate your new Yahoo ID in the Members list. Then click the Edit Membership link (pencil icon) just under your new Yahoo ID. Then click the Change To Owner link near the bottom of the page. Then follow the directions on the resulting page. Only after you've completed the steps in my second paragraph here can you then demote your old Yahoo ID from Owner to ordinary member of the Group you own. And you can only unsubscribe from a Group when you're an ordinary member, not when you're an owner or moderator.