Question: I am doing my first photo shoot of a birthday party for a friend. I wanted to know which lens would be the better option to use for this. 
I have a Canon 50mm f/1.8 prime lens as well as the standard 18-55mm IS kit lens and a 55-250mm IS tele-zoom lens. 
So far, just getting to know my camera I have mostly played around with the kit lens. 
Now I'm not sure which of the others would be a better option.

Answer: 
I'd take all three lenses with me.

Since you don't mention it, I'm going to assume that you don't have an external flash and only the built-in one. The built-in flash will help you in a pinch, but it's not very powerful and it doesn't look very good. I would aim to either not use the flash or use it only for a little fill.

First, if it's indoors and dimly lit, the 50mm may be the best and only solution simply because you can shoot at a larger aperture to get a shorter shutter speed that you can freeze the action.

If you've got a little more light, you can use the 18-55. Personally, I would find the 50mm too long for indoors shooting and would probably use the 18-55 in the 18-30mm range to get some more environmental portraits or small groups.

If you want to work on the long end of that lens -- 55mm -- for some tighter shots, you might switch to the 55-250. On the 18-55 at 55mm the largest aperture is f5.6. On the 55-250 at 55mm the aperture is f4 -- one stop brighter! That may be enough to let you get a shot.
I'd go with the 50mm f/1.8. Assuming you are on a crop-sensor camera a 50mm lens will be roughly equivalent of about 80mm. Combined with the wide aperture this will afford you the ability to shoot wide open or even at f/2 - 2.8 with a great depth of field and sharpness that the 18-55 just won't give you.