he exports ORAENV_ASK, which is certainly used in the file ORAENV.
. ORAENV means that you 'source' the script named ORAENV, that is to say you execute the script, and env variables defined in the script stay defined in your own environment.
EOF is because he is using :
svrmgrl << EOF
which means that the execution of the program svrmgrl will end when EOF will be met at the beginning of a line
IIRC, the ORAENV_ASK variable when set to NO means that the oraenv script will not prompt the user for the Oracle SID that they wish to set, but will instead take the value from the ORACLE_SID environment variable.
If set to Yes, then the script will display the current ORACLE_SID value as a default value in a prompt, asking the user to either confirm the value, or enter a new SID.