It should be possible to install at least the SSO and OID components of OAS 10.1 on a 64 bits Linux system as long as you take the 10.1.4 version. According to the [url http://www.oracle.com/technetwork/middleware/ias/downloads/idm-certification-101401-083012.html]certification information, it is certified as long as you patch it to 10.1.4.3 afterwards.
Note that is a quit typical setup for FMW11g products which require SSO. If you want to use the latest OID version (126.96.36.199) on x64, you will need a 64 bits OS. But you should still be able to install SSO on that box as well and wire it to your OID. Since 10.1.4 is still 32-bits, it should be supported with a 64-bits OS.
Note that you could install your 'infrastructure' on two boxes with OiD residing on the 64-bits box while SSO runs on a 32 bits environment. But I just think that it would be an overkill unless you have strict topology requirements or overanxious network administrators.