Hello, 

I am not sure I have enough information to help you; that is why just ask a few questions:

1. I am assuming you are using AIMMS 64 bits. 
   You can verify this using the AIMMS - Help > About dialog.
   At the top the dialog you'll find the substring 64 bits if it is an AIMMS 64 bits.
   Is this assumption correct?
   I am verifying because the AIMMS 64 bits executables use 64 bit ODBC drivers.

2. Can you open the 64 bit ODBC Driver manager?
   You can do this by typing ODBC in the windows logo.
   

   Subsequently open the driver manager tab:

   The ODBC driver "Oracle in OraClient12home1" should be present in the list.
   Please check spelling carefully; there are different ODBC drivers for ORACLE.

3. If the driver is available, please try creating a User DSN
   from within the tab User DSN using the button
   Add...
   And selecting the driver "Oracle in OraClient12home1"
   Subsequently, follow the instructions of that driver to add a User DSN.

4. If you succeed, please try using the User DSN instead of a connection string.
   If you do not succeed, then please ask your IT department for help as well.

Tip: Instead of manually creating a connection string, please use SQLCreateConnectionString.
An important benefit of SQLCreateConnectionString is that the password is not copied explicitly into the connection string.

Perhaps the following materials are of interest: 

* AIMMS Academy course on Databases & Data Connection: https://academy.aimms.com/mod/page/view.php?id=257

* Which ODBC drivers: https://how-to.aimms.com/Articles/539/539-which-odbc-drivers.html