Try
ssh -t $USER@server006.web.com 'sudo -u http grep -i "Exception:" /opt/local/server/logs/exceptions.log | grep -e "|*-*-*:*:*,*|" | tail -1 | awk -F"|" "{print $2}" >> log.log'
Sudo already runs the command as a different user to there's no need to su again.
Only reason to do sudo su is to have a fast way to start a new shell with another user.