Trust me, I would not subject myself to snarky comments on the forums before searching all over the internet
Snarky answers are just another benefit of posting anything here. My guess is that the documentation for the 10g OMS repository
won't say that you can run it on 11g. But it should work. You need to decide what version you are comfortable running. If you want
to stay with 10g, then use 10.2.0.5, otherwise 188.8.131.52. You don't need to upgrade the database repository and leave OMS at 10g.
You can also upgrade OMS to 11g or 12c.
If you are running 10gR1 or 10gR2 and don't have extended support you are running an unsupported configuration, so do what you want, as long
as it works. If you want support, then run a supported version of OMS. If you want a real answer then you need to create a ticket in Metalink using
you CSI number, unless you don't pay for support...