After deactivating all of my plug-ins and re-activating them one at a time, I’ve found a plug-in that apparently triggered the Strict standards errors. There’s no reason that should work, but it did. Sorry to waste your time, and I suppose you can close this one.
Thanks for your question. I have not tried to go back to the default BuddyPress theme. I use a Genesis theme with Genesis Connect. Had no trouble with the previous hosting company.