Added strength training and gained weight

Don't panic! Muscle is heavier than fat, but any strained or achy muscles are basically inflamed, and inflamed tissue holds water. Give it a few days until any pain/tightness is gone & your weight should come down. Don't forget that your weight naturally fluctuates anyway, so never panic on the basis of a single weigh in. This is a marathon, not a sprint!

When you add strength training, your muscles are going to store extra glycogen and water, more than if you're a regular strength trainer. The way strength training builds muscle is by creating micro-tears in the muscle fibers, then your body fills these tears with glycogen and water to repair them. This extra storage causes the number on the scale to increase for a while at the start; that and the very small amount of muscle gains on a deficit are referred to as "newbie gains". You generally don't gain muscle on a deficit, but those new to strength training may gain a small amount to start.

Take measurements and try not to focus on the number on the scale too much. It's going to fluctuate, and it probably won't go down very much at all for the first month or two when you start strength training, but if your measurements aren't increasing, you're fine.

It's not muscle...you're at a calorie deficit you cannot gain muscle.

Probably not quite true if OP is new to weight lifting... When you first start out, it's possible to build some muscle even at a deficit, but it doesn't work that way for too long. Usually it's referred to as "newbie gains".

It's not fat either...when you're working your muscles the fibers are getting all torn to shreds...they need to repair themselves...they need water to do this...thus your muscles retain water for repair after intense workouts.

... and yep, that's almost certainly what's happening.

Also, most people have natural body weight fluctuations of 2-5 Lbs day to day. I'm maintaining right now and I'm usually around 185 on Monday and 181 on Friday....maintenance isn't static, I have a ceiling and a floor...my true weight is somewhere in between. Likewise, weight loss isn't linear.

... and more yep.

OP, it sounds like you've edged away from the cliff, which is good... Lifting isn't going to cause weight gain while you're at a deficit, although -- if you are new to lifting -- you may see a slow-down in the weight loss as you build some muscle and continue losing fat. Time to take some body & body fat measurements. The changes you see might be more on your body, and less on the scale's numbers.

I'll add that, if you stick with the lifting, don't be surprised if you gain a pound or two the day after you lift. Like it says above, if your muscles are repairing themselves from the strain you've put them under, they'll retain water, and it WILL be enough to show up on the scales.

It's not muscle...you're at a calorie deficit you cannot gain muscle. It's not fat either...when you're working your muscles the fibers are getting all torn to shreds...they need to repair themselves...they need water to do this...thus your muscles retain water for repair after intense workouts.

Also, most people have natural body weight fluctuations of 2-5 Lbs day to day. I'm maintaining right now and I'm usually around 185 on Monday and 181 on Friday....maintenance isn't static, I have a ceiling and a floor...my true weight is somewhere in between. Likewise, weight loss isn't linear.

You can most definitely gain muscle on a calorie deficit if you're new to strength training. It's called neuromuscular adaptation, but most lifters refer to it as "noob gains". In the case of OP, I think you're right on about the damaged muscles retaining water, but muscle building will occur on a deficit too if you're new to strength training.