You only can influence hexes with a circumference symbol in the middle of it.
So you cannot influence Deep Wapr Portal Hexes (but Nexus yes), Black Holes or Nebulaes.
Black Holes and Nebulae, no, but the Deep Warp Portal Hexes do have a circle on them (it would be pretty silly for them to have planets on them that can't be colonized).
So, for both the Deep Warp Hexes and the Deep Warp Nexus you colonize them like any other system. The Anomalies will block you from putting an influence disc down when you explore them, but after the Anomaly (or Anomalies) have moved or been destroyed you can use the Influence action to place a disc from a ship or connected hex you control, or if you have a ship in that hex you can place an influence disc there at the end of the combat phase.