While I admire your enthusiasm,you're all over the place. Asking about combining training for different sports misses the point of both sports. Would you ask about combining training for the 100m dash with the marathon just because both involve running? How about basketball and swimming?
It just doesn't work that way.
If you don't want to train in either sport but are looking to build a good, healthy physical base (gpp) then by all means, incorporate aspects of any physical activities you fancy, but don't think it'll get you anywhere near the results you would in any individual discipline you'd be able to achieve were you to concentrate on one. You wouldn't actually be training for a sport, rather working on general physical preparedness. These things cross over only to a very limited degree with ordinary humans, and I wouldn't benchmark against the very, very few exceptions out there (only Misha Koklyaev really comes to mind).
As far as muscle mass go, for weightlifting you want as a secondary or tertiary consideration to build efficient fast-twitch muscle fibers, which will happen through weightlifting training. Neither of the disciplines you mentioned are very good for that purpose: bodybuilding's hypertrophy-targeted training is only interested in size, while strongman also involves endurace aspects which need and build slow-twitch muscle fibers. Of course, conversion from one to the other isn't completely straight-forward, but the idea is there. The second big consideration would be mobility. Both strongman athletes and bodybuilders customarily exhibit mobility deficiencies which will hinder lifting. Finally, there's the important consideration of technique, which will be hard to develop and maintain if you skip around all disciplines trying to become an all-roynd strength athlete. However, I wouldn't worry about building muscle mass. Look at weightlifters, they are packed eith muscle even if the sport doesn't specifically work to achieve muscle growth. You'll end up looking muscular but athletic, not like a juiced up gym rat.
All that being said, you need to thonk about your priorities and either focus on one sport and treat pther lifts and exercises as supplemental, or give up the idea of training for a sport and work on gpp or whatever you want to call it. But then the question of combining disciplines would be moot in any case.