Can Oracle be installed on Windows without being an administrator? Can the oracle software be installed on windows without having administrator privileges?
No, but there are workarounds

One workaround is to run a virtual machine that has Oracle and only Oracle installed. this has the significant benefit of insuring that the many kernel tweaks required of oracle are constrained within one instance. 

Consider trying deployment within: VMWare Thinapp, VMWare Player (maybe), and I believe VirtualBox offers a user-land install, based on the documentation here.