I have two types of guitars, electric and acoustic and have been playing for over a year. How does one learn to or adjust their strum so that there's not so much sound of hitting the strings (as opposed to actually hearing the note)? Is picking a bad way to get better sound quality and should I be plucking? Please let me know if I need to clarify this question.
If the pick is held too tightly, the sound of it will show up. Sometimes, that's the effect needed. Ordinarily, a pick is feathered (rather like the windscreen wipers on a car), so it glides more smoothly over the strings. Heavier picks will often make more noise than thinner ones. This presumes strumming is of more than just one string - usually most of them.
I still find myself hitting the same issues, even now after 30 years of playing. Mostly with picking individual notes on thin strings on a Telecaster with low action, and it's probably more in my head than anything. Let's worry about your issues instead.
One thing you can do is play with pick angle. Assume this is the string --> | If you play with the pick hitting the string like this --> |, you will maximize your pick noise. If your pick hits the string like this --> —, that won't work for the string spacing or your wrist. If the pick hits at an angle more like this --> / , you'll get less of the slap. For your grip strength and picking speed, I would suggest you don't try this --> \, but if that's what you already do, go ahead.
I think pick angle trumps most other issues, although holding loose or tight is also a big contributor.
In your question you asked "how does one learn to adjust their strum so that there's not so much sound of hitting the strings".
The type of pick you use will definitely have a noticeable effect on pick noise - as will the type strings you use. But your strumming technique can also be a major factor in how much pick noise you get when you are strumming. For more on strumming technique click here Strumming technique for guitar for some quick ideas on proper strumming.
I find that for mostly strumming, a light to medium pick works best (for me). But for picking individual notes (especially fast) a heavier gauge works better because there is no recoil latency. Besides gauge, picks come in many different materials and some are very clacky and some - such as rubber picks - are almost silent.
As Var Log Rant suggest, the attack angle of your pick will have an impact on string noise. There are two ways to look at "angle". One is how perpendicular your pick is to the strings - in other words - how much the pick is pointed north or south.
The other aspect of pick angle is rotation (clockwise or counterclockwise like turning a knob). You will notice a significantly different sound made by your pick if you strike the string as if your pick were a knife and you were going to cut the string by angling the edge of the pick toward the string. Do this with a metal pick (yes they exist) on nylon strings and you may actually cut the string (not recommended - for illustration purposes only).
Another thing that will have an impact on pick noise is how deep you insert the pick into the strings. The deeper you insert the pick, the more friction you will exert on the string as you pluck it with the pick and the more noise you will get. If you have a tendency to insert your pick too deeply, try holding it closer to the tip.
One final note that has helped me use a more relaxed grip on my pick when strumming is using picks with some type of texture on the grip which allows me to use a lighter grip without fear of the pick slipping out of my hands. My favorite pick for this is the Dunlop MaxGrip (better than the original textured dunlop picks). Here is a picture Dunlop MaxGrip Pick. It's almost impossible for one of these to slip out of your hand - no matter how loosely you hold it.
If you prefer a celluloid pick you can use a hole punch to punch a hole in a slick pick and it will make it easier to grip without using a death grip. Depending on the material, you might want to heat the pick with a blow dryer or a heat vent (not a blow torch) before trying to punch a hole in it so it wont crack.
Hope some of this helps. I think you just need to try a little of everything until you find a solution that works for you.
I wish you continued success on your musical journey towards a life long love affair with the guitar. It's a very enjoyable instrument to play - and no matter how much you play, there is always an opportunity to improve your skills.