Musk has a bachelor's degree in physics from the University of Pennsylvania: https://www.snopes.com/fact-check/musk-physics-degree/.
Further, while I share some criticism of the man, many very technical people from companies such as SpaceX and Tesla have come forward with public comments, praising him for "truly grasping the engineering" and "being involved in every technical design decision". Make of these what you will:
Kevin Watson, Falcon 9 avionics:
Elon is brilliant. He’s involved in just about everything. He understands everything. If he asks you a question, you learn very quickly not to go give him a gut reaction.
He wants answers that get down to the fundamental laws of physics. One thing he understands really well is the physics of the rockets. He understands that like nobody else. The stuff I have seen him do in his head is crazy.
He can get in discussions about flying a satellite and whether we can make the right orbit and deliver Dragon at the same time and solve all these equations in real time. It’s amazing to watch the amount of knowledge he has accumulated over the years.
Tom Mueller, SpaceX founding employee:
We’ll have, you know, a group of people sitting in a room, making a key decision. And everybody in that room will say, you know, basically, “We need to turn left,” and Elon will say “No, we’re gonna turn right.” You know, to put it in a metaphor. And that’s how he thinks. He’s like, “You guys are taking the easy way out; we need to take the hard way.”*
And, uh, I’ve seen that hurt us before, I’ve seen that fail, but I’ve also seen— where nobody thought it would work— it was the right decision. It was the harder way to do it, but in the end, it was the right thing.*
Garrett Reisman, engineer and former NASA astronaut:
What's really remarkable to me is the breadth of his knowledge. I mean I've met a lot of super super smart people but they're usually super super smart on one thing and he's able to have conversations with our top engineers about the software, and the most arcane aspects of that and then he'll turn to our manufacturing engineers and have discussions about some really esoteric welding process for some crazy alloy and he'll just go back and forth and his ability to do that across the different technologies that go into rockets cars and everything else he does.
Josh Boehm, former Head of Software QA at SpaceX:
Elon is both the Chief Executive Officer and Chief Technology Officer of SpaceX, so of course he does more than just ‘some very technical work’. He is integrally involved in the actual design and engineering of the rocket, and at least touches every other aspect of the business (but I would say the former takes up much more of his mental real estate). Elon is an engineer at heart, and that’s where and how he works best.
Along with many others.
And you're right he has a degree, although he repeatedly lied about when he received it, and even lied about where he received it, so please forgive people for their confusion.