Here's the scoop...(lifting heavy/fatloss/strength gains)

Yes your right that a lot of it is tied to your diet, but there are other factors.1) your body has to have the right typpes of foods, protein especially to fuel it for the specific event. 2) In order to get stronger, really stronger your typically going to gain weight as a by product of the thickening of the muscles to overcome this new stressor you've placed on it, heavier wights. 3) you also have to remember that there are differnces in the results of lifting, theirs strength, power, and endurance types of lifting. Strength and endurance are very similar. But power, the ability to lift a heavy object a few or only one time is totally different than lifting a weight for 20 to 30 reps. Differnet musclle fivers and much more are involved. 4) you have to be able to break the body parts down to get a more effective workout. We will use the chest as an example. You can not lift wights for the chest without involving the shoulders and triceps. So if your working those parts as well on the same day, assuming you do chest first, those parts will suffer fatigue from the previous chest work. Thats why most pros will cycle through their training and one day will be devoted to just chest, no arms or other body parts, same with arms, no other work that day but the arms. 5) It is very difficult to gain strength in any noticable amount while conducting cardio, or atleast lots of cardio. Again nutrition and body issues also come into play. 6) Weight lifting does help in fat burning but not nearly as much as the cardio does, but thats when you get into the different nutritional issues again with carbs and proteins and such.7) Finally their is the amount of rest needed to fully recover from the workout, it should be so taxing that you need a couple or even several days to recover before you can fully work that body part again. Unfortunately the best way usually is to cycle through your priorities, For example, the next 8 weeks are going to be devoted to heavy cardio with light strength training for maintenance, the next 8 weeks will be devoted to heavy weight lifting for building mass and power with much less cardio.....and so forth.
Please understand that this is not an all encompassing post and there are other issues at play but these are the most basic and general concepts. Further searching and investigating should certainly be done. I hope this helps.

I don't think strength gains need a calorie surplus. If you're trying to bulk up, then yes. But that's not likely to happen to you without testosterone injections.

Are you looking to get stronger or look different? I don't look a lot different after lifting a few months.

I dont lose strength on a deficit. Just broke my PR.
try stronglifts 5x5 workout program

I agree. A lot of programs produce very minimal strength gains especially when on a diet. First, they don't tell you when to, or push you to increase your weight so you end up doing the same weight for 2-3 weeks. Stronglifts tells you to push it as much as possible. Second the rep range on most programs is higher. I just can't seem to increase weight when I'm doing 8-10 reps, but when I'm doing 5 it's much easier.

http://www.myfitnesspal.com/topics/show/560459-stronglifts-5x5-summary

I'd like to start lifting (nothing crazy) to build my muscles and lose fat, too. Add me also please

I'd like to start lifting (nothing crazy) to build my muscles and lose fat, too. Add me also please

You can't gain muscle at a deficet.

I dont lose strength on a deficit. Just broke my PR.
try stronglifts 5x5 workout program

^ This!

I too am at a deficit and up the amount I lift by 10 pounds each week (lift 3x/week full body). Eat protein and lots of it!