usually, when doubling (or tripling, etc...) you won't want to have them all the same volume. Get your main track at a good level, and then bring up the other tracks slowly until they fill up the sound, as opposed to sounding like a "gang" vocal part (unless that's what you want).
Inverting phase won't do anything if it's separate takes.
Also, as you've probably found out, if you want them to sound tight, you have to sing all the parts really tight.You especially want phrases to start and end together. One thing I sometimes do is not pronounce the "ssss" at the end of the line on the extra tracks. I'll only pronounce it on the main vocal part. It will sound and feel weird while you're singing it without the "sss" on those extra tracks. But it will help make the end of lines that end with an "sss" sound much tighter.
A lot of it is simple practice, trial, and error.