Your site security sounds like they try to keep it tight. Not a wrong thing to do these days, given the inherent foibles of Windows as an O/S.
2. Is there any reason I shouldn't be able to "export" data from Oracle and save it to an ASCII file?
ORACLE has an export verb that sends recordsets to ASCII delimited files, usually using comma as the preferred delimiter. Works on tables or views (Access folks call them SELECT queries).
1. How should I approach the IT dept?
Factually. Bring a statement of the problem and the name of the person who assigned it to you. Bring a schema (design) of the tables including relationships. Bring estimates of storage requirements. They will probably want to go through some rigamarole to validate the project and the concept. They will probably also have some sort of chargeback process to assure that the IT group doesn't get an unfunded mandate.
3. If I get access to the Oracle database, can I create my own sql queries and draw data as I need it or will I have to have them do that for me?
Given the tightness of their security based on your description, I'd have to say it doesn't look like you'll be granted DBA rights, which is what it would take to make SHARED/STORED SQL queries. But there are other ways to skin this particular cat. You can always make an SQL file that you can give to ORACLE (through interactive SQL+ or something similar) that can act as a canned query. The difference is that it won't be preanalyzed to determine optimum scan methodology. (I.e. follow the index on table A, then follow the index on table B, then linear scan the result...)
2. Any key buzzwords I should use?
Your main interest is whether they will allow you ODBC access the instance or will force you to limit yourself to SQL+ (interactive) methods. Also you will be interested (though this is not critical; just important) in whether your database would be given its own separate instance or will be folded into the schema of some other instance.
The issues on the one side are that from a viewpoint of security granularity, separate instances are better, and would give you the better chance to be granted the DBA role in your database. In a separate instance, the IT folks can define a special group for you and your users that isolates you. The ORACLE DBAs would have SLIGHTLY less work if they know ahead of time that access to the DB files is limited by O/S security methods. Further, if you were sharing an existing ORACLE instance, they now have to worry about properly setting up roles for your new users that allow them to access your tables but not the other tables in the shared instance. Sort of like having two parallel data sets in a single Access file shared by folks with non-overlapping duties, so the Users group would allow folks to see too much. This would be a lot of extra work for the ORACLE DBAs. They would not like you for doing that to them.
The other side is that ORACLE is - how shall I say this delicately - a bleedin' HOG when it comes to system resources, and every separate instance needs a memory area called the SGA pad (a scratchpad area) dedicated to it. Not to mention the license costs for ODBC and/or for adding more users to ORACLE. Remember, Larry Ellison (the ORACLE CEO) is a Bill Gates wannabe! And he charges for ORACLE products about like Bill charges for Windows components. These resources and the availability of memory on the assigned server will contribute to your IT group's choice in how (or IF) they will allow you to do diddley-squat.