how much memory does the database use? Have you tried the following?
ALTER SYSTEM SET timed_statistics=TRUE;
ALTER SYSTEM SET EVENTS '10046 trace name context forever, level 12';
Then run your queries and use tkprof on the output to see what the explain plans are.
http://marist89.blogspot.com/2005/07/trace-it_04.html
Without seeing explain plans, the query and knowing your environment its just not possible to give a reasoned answer.
I can however say hash partition your tables according to the one field that you most use to access the data. But I can't say that that would be correct.
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