Strength is specific, so saying "I want to be as strong as possible" doesn't really mean anything. Sorry :) How do you define "strong"? Do you prioritize a better 1RM or a better 8RM (or 12RM, or AMRAP at a specific weight)? If you have to choose between adding 2% to your bench or 3% to your over-head press, which do you choose? Would you prefer mastering muscle-ups or doing really maxing out weighted pull-ups? You have to make priorities. Sure, increasing your 1RM will probably increase your 8RM, and vice versa, but if you focus on increasing 1RM then 8RM will probably not increase as much as if you worked on that specifically (which in turn probably would yield less 1RM gains).
Having said that, "general strength" is a valid goal for training (if a bit fuzzy). Incidentally, the exercises you mention are probably what I'd recommend if someone asked for five exercises to train the whole body, so you're pretty much on track. If I were to add one compound lift to the mix, then perhaps barbell row (for a pull exercise with a different angle than pull-ups).
Between these five lifts (or six, if you add barbell rows), there's a ridiculous amount of variations you could do: Front squat, deficit deadlift, incline bench press, chin-ups, single-arm dumbbell press, seal row, ad infinitum. You can add these variations to the mix to hit muscles slightly different from how the "default" execution hits them. For example, doing both regular and incline bench press would make you stronger in different angles, but focusing all your efforts on regular bench would probably make you even stronger in regular bench (at the cost of being weaker in incline bench). A compromise is choosing one variation, which you do for a couple of months, and then change to something else.
You may also want to add isolation exercises or machine exercises to target specific muscles when you've spent yourself on the free-weight compound movements. For example, if you do a lot of squats and your technique begins to deteriorate, you probably still have enough energy to finish off with some work in the leg press and/or leg extension machines to cram in some extra volume for the major muscles. For pull-ups, you can add some barbell curls afterwards to give your biceps some more work, or do triceps pushdowns after bench press.
If you want to look at strongman exercises, farmer's walk is really super useful: Grab something heavy and in each hand, and walk off with it. Great for grip strength, traps and core (hits obliques surprisingly good!). The one-handed variation, suitcase carry, hits core even harder (but is obviously easier on legs and glutes, as you only carry half the weight).
To summarize, there are no glaring flaws in your choice of exercises - on the contrary, it's a very good assortment. There's a bunch of stuff you could add, but adding 20 different exotic exercises isn't what you need to get stronger. If you find yourself on a plateau and unable to set new personal records, you should look at how you train, rather than picking new exercises. Perhaps you should try a few weeks of hypertrophy training (not because you specifically want to get bigger, but because bigger muscles are stronger muscles), or inversely focus on heavy, low-rep lifts to work on your nervous system, or try out daily undulating periodization.
