libpq is thread-safe as of Postgres 7.0, so long as no two threads attempt to manipulate the same PGconn object at the same time. In particular, you can't issue concurrent queries from different threads through the same connection object. (If you need to run concurrent queries, start up multiple connections.)
PGresult objects are read-only after creation, and so can be passed around freely between threads.
The deprecated functions PQoidStatus and fe_setauthsvc are not thread-safe and should not be used in multi-thread programs. PQoidStatus can be replaced by PQoidValue. There is no good reason to call fe_setauthsvc at all.
Read the upstream documentation. For corrections, first check the current version.