One simple and easy exercise you can do is called the farmer's walk. It's a staple of Strongman competitions - usually involving stuff like anvils or gigantic "torpedoes" festooned with 45-pound weight plates. It's also a staple of strongman training, and it could be part of yours.
How do I do it? The basic version is simple - grab two heavy objects and walk for distance, speed, or time. What those objects are doesn't matter too much. Dumbbells work pretty well, but heavy ones get difficult as the weights tend to restrict the range of motion of your steps. Barbells can be awkward to load. Non-traditional weights can be extremely specific - try buckets full of sand or water, loaded suitcases (which often come with ergonomic handles), or whatever. I've done farmer's walks pinch-gripping compact car tires (for training) and 18L containers of kerosene (to get the kerosene home from the store). If the weights are uneven or mismatched, try walking halfway to your goal and then quickly setting them down and switching - it's usually easier to turn around, grab them and then turn back around with them than to swap them on the ground.
Just whatever you pick up, make it heavy. This isn't "heavy hands" race-walking. You want something you can't just casually swing back and forth. The goal is to carry a heavy object, so something weighty that can stand being dropped or set down roughly is ideal.
Walk until you can't hold the weights anymore, then drop them or place them on the ground. That's pretty much it. You can squat down, pick them back up, and walk more, which is fine when you're going for distance or just want extra work. Or if you're "farmer's walk training" is actually "bringing home heavy things from the store" and you can't just leave them on the sidewalk.
Why do I want to do these? Because this is as functional and basic an exercise as you can get. You're picking up heavy objects and getting them from one place to another. That's what functional training is all about - moving furniture, toting groceries, carrying stuff.
As for muscles, they'll work your shoulders and upper back (as you struggle to keep the weight up), your forearms and grip (as you try to hold on as long as possible), your gluteals and your legs (as you walk, probably with short strides, under a heavy load). Your abdominals and lower back will have to stabilize you, and so will your hips. Pretty much the only part of your body that won't work too hard are your upper arms and chest, but they're not wholly excluded, they just don't do too much in the basic version of the farmer's walk.
I'll post again on these, with some variations and modifications you might find useful. But for now, just try grabbing two heavy weights and taking a walk.