Connecting my Mixtrack Pro to my PA system that doesn’t have RCA inputs
What exactly do I need to achieve clean crisp sounds?
A RCA to 1/4 (or XLR, depending on the PA) cable.
Doesn’t always sound clear though and in VDJ I can’t use my headphones via my mixtrack for some reason
You need the search function 
That, and an RCA-whatever cable like ^ said. As for not using your headphones in your mixtrack, make sure you have your mixtrack selected in the preferences I guess. I’m a traktor user, so I’m not too great with VDJ.
USE AND AUDIO INTERFACE TO CONNECT TO PA A RCA to 1/4 (or XLR, depending on the PA) cable.
List all the gear you are using to make it clearer to us
Read thru the manual for your PA. I guess connecting an unbalanced signal to a balanced connection has the potential to create damage on some equipment.
Have you looked into the DI box I suggested in the other thread?