I think you're trying to thread the needle a little too much, and I'm basing that off of a couple of things you've said:
I'm 5'8" @ 137lbs trying to gain weight but trying to stay toned.
I have made some progress in strength but stagnated in some areas
(squats, bench press). Is this normal?
As a comparison, I'm two inches taller than you and weight 185, roughly fifty pounds more than you. I tend to bounce around between 10%-15% body fat. Regardless, I'm barely taller than you and weight a lot more than you, and I fit a size medium shirt. I'm not in anyway implying that we have the same body types or that I'm "normal", but just to give an anchor point to the conversation because I think you need to add on a lot of muscle weight.
It is very hard to do "lean gains", to the point that it's just not worth trying. Honestly the only people I've seen reliably accomplish this were using anabolic steroid supplementation.
There's a common statement tossed around to new lifters:
Chain yourself to the squat rack, drink a gallon of whole milk every
day, and call me in a year.
There's not a lot of magic to this; I'm betting you know this already but you're hoping / believing that you can escape the reality. It sucks, but you can't.
- Building muscles, long term, is better for fat loss than aerobic exercise. Diet trumps all, but on to point #2.
- You need to lift heavy and eat in caloric excess to get stronger/bigger. It sucks, you'll get a little fat, but you need to accept that. This doesn't mean you need to be 500 calories a day over budget. The exact amount isn't dead on, but what is known is that you can't be in caloric deficit. Nailing the number dead on every day is impossible, so you need to go a little over.
- Once you've gained a significant amount of strength/size over a period of months, maintain the weights you're lifting, incorporate interval training and pull your diet in. You'll scrub 1-2 pounds a week. 8 pounds in two months is a huge difference: for your body, that's roughly a 6% body fat swing.
If you try to stay in your "lean gains" mode where you want to get big but don't want to put on weight, you'll basically stagnate forever like you are now. You don't need to eat cheeseburgers every day, but if you're lifting heavy you need to sleep and eat a lot to get bigger. Lift like a crazy man for 3-4 months, scrub the goo for 1-2 months, rinse/repeat.