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: 
Assuming that your camera has an APS-C sensor (18-55mm IS kit lens tells me that it does), the 50mm f/1.8 is probably a good bet for shooting portraits. Typically a photographer wants to use something around 85mm-100mm (on a full frame sensor) for a nice sharp portrait. Since your camera is APS-C and probably multiplies the focal length by 1.6x, you're looking at about an 80mm equivalent from your 50mm lens which gets you close enough to the sweet spot for portraits. Also the Canon 50mm f/1.8 is way sharper than either of the other two lenses that you mentioned. 

Summary: Unless you're using a 5D or 1D, you'll be just fine with the 50mm lens for portraits. If you want more candid, far away shots, try the 55-250, but for sharp portraits, the 50 is your best bet.
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.