Strong is a mean bastard. He likes murder, mayhem, larceny, and Cannibalism. More problematically, he doesn't like picking locks, hacking terminals, or using dialog to solve problems.
I'd like to max out Strong's approval for my Wanderer, but I'm not particularly keen on just going on a crime spree, and don't want to invest a ton of perks in getting the Endurance to try being a Cannibal. Which leaves me with dragging him along while I do some quests, since he does seem to like being helpful to people (especially if chems are involved).
So, what readily accessible quests will offer tasks and dialog of which Strong approves (i.e. violent or aggressive), without compromising the resultant outcome of the quest, while also requiring a minimum of hacking or lockpicking?
Best Answer
The wiki says Strong (and I have noticed that Curie and Hancock as well) likes to be out and kill things... And that gains approval even if it does not seem that way. Allow me to elaborate; you can get strong to adore/idolize you simply by going out, exploring and killing. So you do not necessarily need to do things your companion "loves" or "likes" for him to gain approval. I can confirm this is true for Curie and many people seem to agree it works for Strong too.
So my suggestion? Go to Diamond City, check the bounty board (that's left to the guy selling "swatters") and do a lot of them with him. Most bountys just requiere you to go somewhere, kill the boss of the place and loot. So do that, but remember never to lockpick.
What I am trying to say, is that the following is without logic, but still happens: I left Codsworth at Sanctuary, and you notice that he "loves" when you customize a weapon or an armor, and so I intentionally only customize things at Sanctuary to have him "loving" it, but how can it be that it took me 8 "loves" just to reach the first level of approval, and with Curie i have barely got one love and 4 likes and she is already in 3rd level of approval with my character? Well it seems that "hanging out" and "watching each other's back" raise approval silently. So you most definetelly want to take strong with you to some raider camps and gunner strongholds. He will "approve" just being there as a team teamwork. I hope someone with PC and console commands may explain how does this works (because it does) in terms of how much time spent, or xp gained, or enemies killed it takes to get "likes" equivalent approval... But that's that.
If you have trouble finding the bounty board, go to the mayor's office and ask the secretary for work. The bounty board will appear on your map after that.