Reception voids with two omni antennas at 90 degrees
It depends on how the two antennas are wired. In general, if you're feeding two antennas with the same signal, you're not going to get "omni" coverage, you're just going to shift the directionality to a new angle. For example, a single loopstick has a figure-8 pattern, with nulls in two directions. Two loopsticks wired in parallel will still have a figure-8 pattern, but the nulls will point in different directions.

The same thing applies on the receive side. If you wire two antennas to a single receiver, you're just going to shift the directionality. To get true omni coverage, you need two separate receiver front-ends.

If you can phase-shift the signal to/from one of the antennas by 90&deg; relative to the other, you can create a "circular" polarization pattern that will help mitigate this problem. Now the nulls will be in the plane of the PCB.