Variables are interpreted in a here doc (<<...), so you need to escape the ones you don't want evaluated yet.
su - db2prd<<EOF
PARMDATE=1111111
echo parmdate
echo \$PARMDATE
EOF
Or better, quote the delimiter (here EOF) to tell your shell not to perform expansions inside the here-document:
su - db2prd<<'EOF'
PARMDATE=1111111
echo parmdate
echo $PARMDATE
EOF