I solved my own issue but I wanted to post it here in the forums to help others as I haven't seen this posted here:
My organization recently created a new VM and installed a Power BI Data Gateway on it. The Data Gateway is active and I can see a success message showing that it is active. I installed Oracle ODAC for 19c so I have the Oracle Client up and running and the server meets all the requirements listed in the Oracle connection document.
I am able to create a 64 bit SYSTEM DNS ODBC entry and successfully connect to our Oracle 18c databases. When I go to create this source under the gateway through the service via ODBC, I receive:
"ODBC: ERROR [IM002] [Microsoft][ODBC Driver Manager] Data source name not found and no default driver specified"
When I try and make an Oracle connection, I receive:
"TNS:could not resolve the connect identifier specified"
I have a system environment variable set up for TNS Names. I can %echo% that variable and see that it is successful and is located here: C:\app\client\username\product\19.0.0\client_1\Network\Admin\TNSNAMES.ORA.
It's like the gateway isn't recognizing my tns location or the system variable.
ODAC for Oracle 18/19 needs to be tweaked to work. Everything in this link worked for me. Just be careful in step number 4 that you don't have spaces between the command arguments.
(Example: OraProvCfg /action:config /force /product:odp /component:dbproviderfactory /frameworkversion: v4.0.30319 /providerpath: Oracle.DataAccess.dll should have no spaces between the colon and the argument.