I used the same party as you and I had only brought 2, and although that's not quite as bad as your situation, I still managed it. It's tough but do-able.

If Celes has Ice 2 or Ice 3, then use that, and have Edgar use Chainsaw. Another thing I did was to cast poison on my characters, because the poison damage does less than any attacks made on them, and this can mean the difference between killing them and getting them to near-death, although you'll have to be handy with cure moves.