If you have successfully installed Oracle, and can connect to the database from SqlPlus, that's all you need.
Don't use ODBC to connect to Oracle. Oracle provides JDBC thin drivers, which are far better than ODBC and don't require additional setup beyond the connection string. Our Oracle FAQ contains links to JDBC drivers and also some info on the format of the connect string.
There have been a lot of problems with Oracle 11g XE on Windows 7, as the 32-bit version doesn't always install or work properly and there is (still!) no 64-bit version. Check in your Windows services to see if the database (OracleServiceXE) and TNS listener services are running (OracleXETNSListener). Then use JDBC to connect to the database using the Oracle thin drivers.
If you can't get XE working, you can still try installing the Windows 64-bit version of the standard Oracle 11g database instead, which runs fine on Windows 7 (you'll need lots of RAM for this, especially as you want to use Eclipse as well!). The download site is here, and there are some introductory tutorials here.
Incidentally, for your database work I strongly recommend you download the free SQLDeveloper tool from Oracle, which gives you lots of Oracle functionality independently of your Eclipse DB plugins etc.