Doesn't it just work if I 'get' the newer Oracle.DataAccess DLL?

Most probably, try it out please, and send us your feedback.

yes, but the thing is that I can't find any link to download that DLL. I've been searching for weeks

What about the link I've posted earlier? http://www.oracle.com/technology/software/tech/oci/instantclient/htdocs/winsoft.html

That link has other DLLs.

Here is a screenshot

http://screencast.com/t/45muKTKFD

Yeah, I can't seem to find it too.

Maybe you should try the latest 11.x.x one: http://www.oracle.com/technology/software/tech/windows/odpnet/index.html

Does ODAC 11.1.0.6.21 works with Oracle 10g and LLBL 2.5?

It should work with previous database versions.

If it doesn't work with LLBLGen Pro, please check this blog post: http://walaapoints.blogspot.com/2007/06/odpnet-llblgen-pro.html