Can I limit access to postgresql 8.4 databases via ODBC on the server side?
ODBC is a client tool and does not affect the way that Postgresql verifies access.   I don't know if its any different for a postgresql server on windows, but in linux, there is a file called pg_hba.conf. This file is usually located in the data directory of the server install.  In Linux, you typically find it in /var/lib/pgsql/data/.  

This file allows you to define which ip addresses can access your postgresql server and how they may access it.  Types of access include trust (no password), md5 (password), etc.  

So for example, if your access users are on say 192.168.0.10 and you want them to use a password you would add this entry.

# TYPE  DATABASE    USER        IP-ADDRESS    IP-MASK             METHOD
host    all         access_user         192.168.0.10    255.255.255.255     md5     


In postgresql you would then have to create the user and give him the ability to login. 

1. psql -d nameofdatabase
2. CREATE ROLE access_user WITH LOGIN PASSWORD 'jw8s0F4';
3. GRANT SELECT ON nameoftable TO access_user;


Good luck