Air-dodging and actual DI are not directly related. You basically have 2 options: 1. Air-dodge as soon as you're hit to regain control of your character, and then recover with a move that has momentum that isn't in the direction you're flying. 2. Air-dodge or not, hold the control stick perpendicular to the direction you're flying to cancel out some of the momentum. Normally it'll be a combination of these two. Generally I air-dodge, then DI, but if you look at it neither of those are beneficial to each other. Air-dodging is a force of habit for me. For examples of each of these: 1. You're on one end of FD, and your opponent has just F-smashed you across the stage nearly horizontally. Air-dodging right after you're hit allows you to regain control and you have options as to which move you want to attempt to recover with. A risk-taker would try and throw out a tether as they pass by the corner of the stage, which is an IMMEDIATE stop as you catch the ledge. However, someone else may prefer to DJC some of the momentum, as it's a much safer bet. 2. This is very specific, but it makes its point. Pikachu hits you with a D-smash while you're at 100+ percent. Why bother air-dodging this when you know you're getting sent straight upwards? Merely holding left or right cancels out about 1/4 of the momentum, and you can very clearly see it as you fly towards the direction you're holding, which is not a natural direction for Pika's d-smash.
Sorry that was quite long-winded, but I just wanted to try and clear it up for everyone. In conclusion, there is no DIRECT correlation between air-dodging and DI, as air-dodging is merely used as a tool to regain control of you character much quicker than normal, which allows to perform recovery options. DI on the other hand, is the natural movement of your character in a direction that is not the same as your given momentum from a particular move.