Yes adrenaline does play a huge role in allowing the human body to do things that are normally not possible. But there is more!
When we are faced with stress, like trying to catch a train or running away from being shot the brain receives that in the form of stress. The stress and emotions we are feeling, like fear or anger stimulate the hypothalamus in your brain. This controls your stress and relaxation in your body. When the hypothalamus recieves the message of stress then it sends out messages to the adrenal glands causing the sympathetic system to react by sending adrenaline (epinephrine) and noradrenaline (norepinephrine), hormones to cause the body to react stronger than it would in a normal everyday situation. These hormones cause these hormones raised heart rate, increased respiration, dilation of the pupils, slowed down digestion and allow muscles contraction.
Adrenaline comes from the adrenal medulla a region of the adrenal glands that is above your kidneys it allows blood to flow easier than normal in your body allowing a higher percentage of oxygen to be in your blood, thus allowing your muscles to be able to function and be stronger to out run someone, or in some amazing cases allow people to lift cars off hurt people and allow humans to fight for their lives against bears and survive. Also when adrenaline is released it speeds up the the conversion of the body's fuel source glycogen into its fuel glucose faster than normal, allowing the body to be stronger yet.
The strength of the person depends on many factors, like age, gender, ethnically, physical fitness, and the ability of their body to react. A body builder would be able to react better to adrenaline than a small child would. There is many factors that would determine the strength of a person feeling adrenaline.
There is no set limit really to what human strength can do with the help of adrenaline. Unfortunately no one has bothered to really test the limit of the human body. Obviously harm to the body, like breaking of bones, tendon damage, ect would be a limit, but no one has really tested the idea. Someone really should.
In theory adrenaline overdose could happen, because too much of anything is bad for the body, but there has been no recorded cases of death or harm caused by adrenaline overdose as far back as 1900. Before they didn't keep very good records that I could get to.
Hope that answers your questions. =]