So, what will ten minutes of jogging do to help someone who isn't dieting?!

It's good that you are slightly active I guess, but like 90%(90% of statistics are made up on the spot x[]) of losing weight/changes to your body are in the diet. It's a shame that you find that it is too difficult to give up bad foods you are addicted to because that is what will make or break you. First off there are 3500 calories in one pound of fat. The only way to lose weight is to create a calorie deficit which is consuming less calories in a period of time than your body needs in that period of time and THE BIGGEST PART OF A CALORIE DEFICIT IS EATING LESS. The cardiovascular exercise burns more calories to add on to your deficit. So if your body needed 2000 calories in a day to maintain your current weight, and you were on a 1500 calorie diet, your deficit without cardio would be 500 calories. This in one week would be about 3500 calories/1pound lost (500x7days). Now lets say that you ran/walked for 20-30 minutes a day and burned 200-400 calories EXTRA a day. With the extra 200-400 calories a day that is an extra 1400-2800 lost in a week, which can almost be a pound.

I really feel for you about your "addiction"(it really can be) to the bad foods you eat. Breaking your romance with these foods is the hardest part of weight loss and it is what stops many dead in their tracks. It took me months of ******* up with my diet to finally get my weight loss going and I did reach my goal :D. A very good way to start a better diet is to eliminate all the bad foods from your house(O NO YOUR HARD EARNED MONEY, o well it was wasted on unhealthy junk anyways), which means THROWING THAT CRAP THE HECK OUT. You can find much information about healthy, tasty foods online that will help you out. It will take awhile to lose your cravings for fried/greasy junk, candy, etc. but it's worth it in the end. I like to think like I used to be an alcoholic, "my name is charlie and I haven't eaten fast food in 4 months."

Another flaw that I see in your methods is that you seem to think of dieting as some gruesome activity that you should stop once you are happy with your body(I could be wrong). I don't like the term dieting, I prefer eating healthy as a long term goal. Trust me once you have been eating healthy foods for an extended amount of time your body won't want junk food anymore, it will probably even make you sick to eat fried/greasy foods.

So to answer your question more directly:
Will ten minutes of jogging help someone who isn't dieting?
Probably not at all, try and work your way up to 20-30 minutes of at least light cardio at first, or after you have finished jogging try and walk for another 20-30 minutes(it really does help!) This is because 10 minutes of jogging will probably just burn you around 100-150 calories where 20-30 minutes would burn you around 250-400+(depending on how hard you try)
And the biggest reason that it won't do much is because you most likely won't be fueling yourself with enough good quality foods to feel like keeping it up OR you will just be eating too much for it to make a difference in general. Don't give up on the exercise though, who knows maybe you will decide to keep up a diet some time and having the ability to run for a good amount of time will give you an advantage then. Good luck.

first hand experience with the subject and I have done a lot of research

Nope. If you want to make yourself healthy you have to have a high intensity work out. The jogging should be a warm up, which is why you can keep up with it. Smoking will make it harder for you to get through a good workout if you have damaged lungs, but not impossible. If you smoke as much as you drink, it shouldn't be a big deal. As long as your diet doesn't destroy your blood pressure or cholesterol, you'll be fine. You can pretty much eat whatever you want as long as you workout to compensate for it. The reason for eating healthy is because it gives you the right energy to work out and recuperate from it. Personal advice: smoke rarely(or quit), your drinkings fine, have an actual work out 3 or 4 times a week(jogging is the warm up) and eat what you want as long as your portions are reasonable

If you jog everyday, you might just about hold the weight off, although, I don't think you will continue for the long term, unless you really love running and show commitment by also eating healthy. I lost a lot of weight last year by running 10 mins a day everyday. I could eat alittle of the rubbish stuff, but not too much of it. everything in moderation.

If the jog is increasing your pulse rate and making you slightly out of breth then its working. Try and increase it to 15 or 20 minutes a day, done in 2 or 3 smaller sections.
It will make you generally more fit, but not healthy.
Try and drink plenty of water and eat fruit and veg or vitamin suppliments!

Ok I'm happy that you have began to do some form of physical activity. I personally say that what you're doing is helping slightly but the significance is very minimal due to your smoking addiction. I would encourage you to do reduce and better yet eliminate smoking altogether. I do understand the struggles with quitting drugs and alcohol because I used to have these struggles. The fact of the matter is when you want to change you feel like you can't because things come along and make you not change. You must expect and accept that you will have opposition when you begin to change your life for the positive but you must not give into the temptation or you will mostly give up and go back to your bad habit.

About exercise maybe you can run for 10 minutes and speed walk for 20 mins. You can gradually increase your running to up to 30 mins daily.

Many people have stopped a negative addiction their own way. I chose to go to Jesus. I chose to follow his way. I don't know what your beliefs are but I know from experience that by following his word our circumstance will change for the better. Good luck and God bless.