A couple of thoughts...
1. You could export the data into flat files and write a SQL Loader program/parameter file to load the data into Oracle. If there are a lot of tables or there is a lot of transformation to be done, then this may not be too practical.
2. If there is a driver for the Quadbase product, you could write an application to do something similar (with similar caveats).
3. You could look at using a SQL DTS package (if you have SQL available to you). If there are a lot of tables, but not a lot of transformations, this could be an easy approach.
There may well be other approaches...these are just a few to get you thinking...
Have you hugged your backup today?