I'm very sorry about your MS diagnosis but please don't panic about it. Many forms of it are very benign and will not necessarily affect your lifestyle too much.
As for telling your employers, I think redcpxs's idea of a lighthearted comment about being pregnant is a good idea. They will obviously be curious about what your medical condition is and if you really want to be offered a permanent job with them, they're going to want to employ somebody they can trust. I think you should be honest about your condition. They probably would not want to employ somebody who is pregnant because of the future disruption it would cause in the business, especially if it's a small company, but MS can be lived with and they would probably respect you for being honest with them up front.
They are now possibly worried that you're going to try and deceive them by not being open with them until after they might have offered you a permanent job and in their eyes, this will make you untrustworthy. I'd be inclined to be totally open with them and say that you would really love a permanent job with them but if they were thinking of offering it to you, you wanted them to know that you'd just be diagnosed with MS. Tell them you hadn't said anything immediately after the phone because you just wanted a couple of days to come to terms with the news before talking about it because obviously it had come as a blow. I think they would "buy" that explanation and respect you for being honest. They will also accept that you have been trying to look at it from their point of view as well. Good luck. I do hope you get the job. Let us know how things work out.