That is pretty weird, i do that all the time and it is working just fine for me.

The omnimaga.org / www.omnimaga.org having different sessions still exists for me...
EDIT: actually, nvm, without www is a redirect to www now

On your side, make sure to never forget to use the www and to not click any link that lacks the www. On Omni's side, they would need to fix the sub-domain names.

I think it depends on the type of redirection you do with the www and non-www subdomain. If you make both of them point to the same IP and nameservers your browser will not see the difference between www and non-www, just like I did on my domain. For example, you can access the BrainPuff interpreter by entering either http://www.lunarfire.info/brainpuff/ or http://lunarfire.info/brainpuff/. Both lead to the exact same page, but your browser will think those two adresses as being different. After all, I could make www.lunarfire.info point to www.omnimaga.org and lunarfire.info point to my webhost, and there would be no problem at all.

What you would need to do on Omnimaga is a either an HTTP or HTML redirection. The first works by adding a redirection header to replies on requests sent to the non-www domain, and the second would be to add a meta redirection tag in the code of the non-www subdomain. I personally recommend HTTP redirections, as the redirection will be un-noticeable to visitors (versus the HTML redirection where you would see it a second or two).