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 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.