Understanding Oracle database and ODAC installation
Oracle XE is kinda special in that you typically install the server and client on the same machine. Logically, they are separate, but it does make things a bit harder to understand. For that reason, I will refer to other experts.
The folks at ORAFAQ have information about the TNSNAMES.ORA file. My personal strategy is to make all my TNSNAMES.ORA files the same, so there is no opportinity for confusion.
ODP.NET is for...
.NETuse, while ODAC is "native" (OLE) and provides more tools than you may have with just ODP.NET. Use whatever works for your needs.For most cases, you would distribute the Instant Client. The Full Client is more useful for developers. Refer to the documentation and FAQs for details. You can have multiple clients on one machine, so I'm not sure what the problem is.
Restart the machine? Did you add the appropriate library/libraries to your environment?