Are you looking for gym movements that would have carryover to strongman? It sounds like that is the case, but then you mentioned 'just for fun' and so I wasn't sure if you actually planned to do any training/competing with implements - and if not then it would not really make sense to "train like a strongman".
In general most strongmen focus on deadlift / deadlift variations, front squat, push press / strict press / push jerk, incline bench, heavy rows, and conditioning (could be 20 rep squats, medleys, etc.).
Depending on where you live there may be gyms within driving distance that have some implements that you could train with every once in a while. There are also some things that you can acquire/make fairly easily if you have space at home - giant tires (usually free), kegs for loading/carrying/pressing/tossing, sandbags made from a military duffel bag, axle bar made from pipe, tire sled made from a car tire, river rocks for lifting/carrying/pressing, chain yoke made from pipe with chains, farmers handles made from pipe or pipe and 4x4's/6x6's, etc.
Hope that this helps!