Strength is strength. The word 'functional' became a buzz word a while back but is largely nonsense. When you're teaching your body to generate maximum strength/power, it doesn't care whether you're lifting a bar, applying force against a resisting opponent or pushing your car in mud.
You can definitely incorporate cycles where you focus more on strength, conditioning, or speed/power. Attributes such as load, volume, and frequency will largely shape how your body responds. Doing 500 body squats will build great anaerobic conditioning. Doing heavy 1-5 rep back squats will build great overall strength. Doing pistols will improve your balance, proprioception, symmetry, etc.
In a pinch you can do bodyweight squat variations to build some base level strength. If you have training partners, you can do fireman/prison squats to go beyond bodyweight squats. You can also do plyos or jump squats after heavy squats.
For a basic strength program you can incorporate squats by doing something like starting strength as previously recommended or an easy scheme where you work up to a moderately difficult 5 rep set. Do that once or twice a week. Aim to improve in some way every workout (add weight, reps, or sets).