You're right there dude.... a skinny guy with m(o)(o)bs looks very odd. Been there done that!
Here's what you've got to do my man.... Join a gym and exercise at least 3x a week. Cardio and resistance training. Join a program such as Weight Watchers (it really does work!) and follow the program. Get down to about 210/200 lbs and then consider corrective action for your gyne.
No. Having stretch marks does not mean that your skin has lost its elasticity. Your skin has the ability to expand and contract. When you expand the skin beyond its limit, it tears. As a result, you get a stretch mark scar. When you lose weight, your skin will contract. Using a balloon as an example... If you put too much air into the balloon and stretch it beyond its limit, you will see it start to tear (stretch marks). If you let the air out, it will shrink back close to its original size. Your skin is very similar to the balloon.
Have you posted any pics?
What country do you live?
GB