Yes, both X-10 and HLC can used on the same system, but, they must be on separate House Codes. You can not use both X-10 and HLC on an Omni LT, because the Omni LT has 1 House Code - you can use one or the other type of lighting, but not both.
The J7 port on all of the Omni, Omni II and Lumina families of controllers is dedicated for use with a X10 transceiver. It does not otherwise need to be configured. The transceiver will only work with X10 switches.
The PIM (36A00-1; included in most promo kits) plugs into any RS-232 serial port configured in Setup>Installer>Expansion as “UPB”. The jumper below the port must be in the RS-232 position. This module will only controls HLC/UPB switches.
Omni and Lumina controllers with multiple house codes (i.e. other than the Omni LT) may control both HLC/UPB and X10 switches. In the Setup>Miscellaneous menu, and on the Control tab if using PC Access, set HLC house codes to HAI Lighting, other UPB switches to UPB, and X10 switches to Standard, Extended, or Compose, as appropriate.