Tosa,
I would like to initially use it as assistance to the main lifts (powerlifting) and for something new. My goal would to be to compete in strongman and maybe highland at some point. I have never done a powerlifting comp, and will probably start there. I also probably only meet the minimum requirements for beginning strongman training as I do not possess anywhere close to a bodyweight press, but my squat and deadlift are starting to come along (squat is my focus).
TF: I have been to that site some good info there also, thanks.
You certainly can use strongman exercises as assistance for powerlifting, but keep in mind that deliberately choosing strongman exercises may mean not doing something that could be more optimal. Some of the following I haven't tried, and I don't regularly use strongman type exercises in my training, but I can talk about what I've read and observed at my gym.
Atlas Stones, for strengthening the back.
Farmer's walks, for grip, abs, and traps/upper back.
Log or fat bar presses, obviously as pressing assistance.
Prowler sprints and sled drags for conditioning.
Since it's assistance, the focus is usually on volume, so most of the time the intensity is medium. Typically done at the end of the workout, or on a day where strongman and some high intensity conditioning work is done, although the presses can fit in wherever. I've seen other stuff done, but that's what I've seen done with any consistency.
Anyway, this is just some suggestions of what you could try, or maybe to give you ideas. I'm not recommending this as right or wrong.