I have a problem with the word "limp" and "hobble". I do not know which word is appropriately used when it comes to context because I do not know how the words differ from each other. Can we use them interchangeably? Do they have the same meaning? How do we differentiate the word "limp" from "hobble"?
Limp means that you are favoring one leg. A person that limps puts most of their weight on one leg and kind of drags the other along.
A hobble is someone who is walking weird, struggling to walk (both legs bad), and often someone who is just really slow (often because of injury/handicap).
Edit: Mari-Lou has a point in the usage of hobble when a person hurts one ankle. This is common especially in sports. The use of hobble would be right because the person is not dragging the bad leg along, and they generally just look slower and like they may be injured in some way. Lots of athletes hobble around the field/court, if they are actually hurt bad enough that they need to limp then their playing is a bit more heroic.
The definitions you have quoted don't explain the difference.
A hobble in this context is to walk with a handicap or injury.
They do overlap, but the limp is uneven.
There are other meanings for hobble shown in the link also. Notice that this answer uses three different sources. If one source isn't clear to you, look at others :-)
I think the difference is also one of degree. A limp is an uneven gait in which the compensation is largely limited to the legs, but the head and torso move approximately normally.
A hobble is more severe. The legs alone are unable to fully compensate and the entire body moves up and down to take the weight off of the injured leg.
In the examples of a limp, the limper is but little impaired, going on for long distances and doing work without further characterization of the movement. Hobbles, however, are the movements of cripples, camels, rheumatics and those requiring sticks to aid their movements. This is born out by the other senses of both words. Hobbles have more exaggerated movements. Limps are mild impairments.