Interestingly enough, Outlook 2010 worked using automatic configuration (meaning when you hit "add new account" you just enter "your name," "E-mail Address," and "Password" then click "Next") for me last time I tried it, but here are the latest manual IMAP settings for on or off-network use:
465/SSL will work here also (see our email server names article), but 587/TLS was defaulted by the autoconfig.
And it works like this on our desktops, which are off the Cox residential network. When it's set up to work off-network, it automatically works on-network.
If you're continuing to have problems, double check the username and password (case-sensitive password, no "@cox.net" on the username) and also make sure webmail is letting you log in.
EDIT: We did away with the geographic server names a while ago. We still have east and west servers, but we autoselect them based on your IP in order to simplify the SSL setup and off-network usage.