Would a join help you more so than a relationship class?
Add your data to ArcMap. Right click the data that has the spatial column (the feature class that can be symbolized). In the Joins and Relates section, add the join to your table with the extra information. Once the join is created, right click the feature class again in ArcMap table of contents. Go to properties, the symbology tab, then choose Categories. Do you see your Oracle table fields in the Value Field Drop down?
I just tested this in ArcMap 10.6 beta:
Create new feature class in Oracle 11g geodatabase.
Use SQL to create an Oracle table (not registered with geodatabase), and insert data.
Add the feature class and Oracle table to ArcMap 10.6.
Create a join on my id columns, keep all records.
Open layer properties for the feature class, Symbology tab, Categories.
I can use my Oracle table fields to symbolize.
Questions/Clarity needed:
If this workflow is different from your own, please clarify.
Please also clarify if you are working with any data that is not registered with the geodatabase (Can verify this in ArcCatalog, right click the table/feature class-> Properties-> General tab...if it is not registered then there will only be 3 tabs...there will be more tabs if it is registered).
What version of ArcMap are you using?