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 have the same 3 lenses that you mention with the Canon 550D and a Metz flash. I've found that the 18-55mm kit lens does quite well when stopped down to f/8 and used with the flash indoors (bounce flash in particular). Make sure that you have the portrait picture style preset in use if shooting JPEG to make the portraits look warm. The lens covers the ideal focal lengths for indoor portraits including group shots. You can also get by without flash by bumping up the ISO - 1600+ is usable on the 550D, especially if you plan to share online exclusively.

The 50mm f/1.8 prime is also quite useful for individual and small group portraits. You can use wide apertures to blur the background. It gives pretty sharp results without having to stop down, and you can do without a flash to get decent shutter speeds.

Since you are planning to shoot a birthday, make use of the burst\continuous shooting mode to capture the important moments like cake cutting. This is also handy for group photos to reduce the chance of capturing people with their eyes closed. The prime again helps here, as it can be used in burst mode without a flash.

Also, be careful when changing lenses during the party - good time to get unwanted particles into the camera\lens.
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