I'm NOT a strongman competitor. But I incorporate strongman events as part of my GPP training for my sport. Plus, I often train with two yahoos that competed in the 08 WSM - Brian Siders and Phil Pfister.
I know a lot of how Brian and Phil Train. Brian doesn't count as he's not from this planet. Dude benches three times a week and squats and deads twice a week. Phil is more human in regards to capacities, work load, and frequency. He's an enormous human being with an ungodly bone structure.
I incorporate stone and log lifting/carrying/pressing into my GPP. I also do axle clean and press for the ocassional "mix it up" with my olympic training.
I hate tire flipping. I've got a enormous bugger in my back yard that my wife "keeps on waiting" for me "to use."
I really like any time of farmers carry. I don't go overly heavy on these movements as I'm not a competitive strongman.
I also love Conan's wheel. Every time I get an opportunity to event train with Phil, I make a couple laps with that implement. It's excruciating in a good way.
Ask some more specific questions and I might be able to provide you with some insights.
All the best,