Hi Mouseam, Thanks for your reply! Keep in mind I'm not a DBA or Sys Admin so my understanding of these things is minimal.
We've been looking into things further after discovering this problem and found we're pretty sure it has nothing to do with privileges. What I said in my first posting turned out to be incorrect.
Here's what we know at this point. When creating a new table everything works as it is supposed to (text fields = VARCHAR2, etc.). However we have some tables that show up as "SDE Table" types and some that just show up as "Table". If we add a new text field to these tables it is NVARCHAR2. Important to note, we do have 2 database instances but these tables are in the instance where the DBTUNE table had the setting for UNICODE_STRING FALSE and can't be modified from the other instance. These tables say they are registered with SDE, but I believe since they aren't SDE_Table types, they are not using the DBTUNE table when changes are made (adding a field).
After this info., do you have any ideas? Do you know the difference between a "Table" and "SDE_Table"? Could it be that the table was created outside of Arc?