To add to what Roger said:
Regarding the "side to side (roll axis)".
1. As Roger said, the fin size will make a difference on how you "roll" the board.
2. However, speed is the most important point. Regardless of fin size or lift, it you don't have much speed (slow plane), you may still need to "tip your board so the upwind rail is lower" to get upwind. If you have really good power and speed (regardless of fins size), then "tip your board very slightly, lee rail down".
I think the key to going to windward on short boards is speed, and most novice and intermediate sailors aren't comfortable with the speed necessary to "ride the fin" and raise the windward rail. It takes time and practice to discover how this works, but you will be surprised at how well you can go upwind on a small board.
Anytime you think you have good speed, try to head upwind by sheeting in a little and pressing with the toes on the back foot to roll the lee side down. Do it for short bursts to get a feel of "riding the fin". You will know when you are getting it right since 3/4 of the board will be out of the water. If you immediately slow down and begin stalling, you don't have enough speed. If you point too high into the wind, you will stall no matter how much speed and power you have, so it takes practice to find the point where you maximize your upwind performance without stalling the board.
Formula 160; iSonic 111; HiFly Move 105; Tiga 263; '85 Mistral Superlight.
Maui Sails TR 11.0; 9.2; 8.4; 7.6; 6.6; Maui Sails Switch 6.0; 5.2; Maui Sails Global 4.5; 4.0.