I think database locking and all does not come into picture till the time you are just reading the data. As a matter of fact in my handler I try to run a stored procedure which has data insertion but it happens only in oracle global temporary table. These tables are used for parallel run and insertion can happen simultaneously in different sessions, in fact each session gets it own copy of global temporary tables. If I try running my stored procedures from two different instances of TOAD(interactive utility to work with oracle) the stored procedures run parallely independent of each other.
I just tried running TOAD and my program together and they did run without problem. Indication oracle for ODBC driver also is capable of multithreading. However I am not so sure about the way 'oracle ODBC driver' and labVIEW interacts?