In Oracle how do I put certain tables or partitions in a different group so the rest of the db can be brought up with OR without them?
Put the tables in a different tablespace. Then you can put the datafiles under a different location/group/naming scheme to the rest of the data, and configure your backups to ignore these files.

If you need to recover the database without this data, you should drop the tablespace with the database in mounted mode:

startup mount;
drop tablespace your_unneeded_data including contents;
alter database open;