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 would suggest 50 mm and 18-55. Below are the reasons

1. 50 mm is great for portraits.
2. if the party is not well lit, you will not have lot of difficulty with 50 mm, but 18-55 will have trouble in low light.
3. 50 mm will not be wide enough to cover medium to large groups. That is where the 18-55 is going to help.

Having said that, if you don't have a second camera, it is going to be a pain to keep switching lenses and you might miss the moment.
If I were you, I'd shoot most pictures with the 18-55 and then after all the action is over, shoot portraits with the 50mm