In order to drive in an arbitrary direction with omni wheels, the wheels must be independently driven (four gearboxes for four wheels) and not all pointing the same direction. The angle does not actually have to be 45 degrees; if you will be driving forward/reverse most of the time and just need the "strafe" motion for minor adjustments, you can angle them at (for example) 30 degrees.
To search for various configurations of omni wheels, I suggest:
- omni tank (4 wheels on two drive trains, no sideways driving)
- kiwi (three wheels, most commonly oriented 120 degrees apart)
- killough (3 wheels in Vex and FTC, but more commonly 4 wheels at an angle in FRC)
- slide or H drive (5+ wheels on 3 axes); omni tank plus one or more wheels mounted perpendicularly, most commonly forming the letter H.
Another variant of killough that we played with diagrams o a few years ago had four wheels at the corners of the robot, each aligned with a different side. This should drive similarly to regular killough or mecanum, but be more stable due to the larger wheelbase and not require non-square cuts. See attached image. (Again, we just brainstormed the idea; we never tried to build one.)