The cheapest way to get to Universal is to use the Lynx bus system. It's about $3.00 each. However, it involves a transfer and many bus route stops and can take up to 3 hours each way.
However, if your looking for direct transportation at a reasonable price, then I would look into renting a minivan for 24 hours from Alamo or National. Just keep checking for deals. You can pick it up at the Dolphin or the Car Care Center on Disney Property. Probably less than $100 for the 8 of you.
Or you can look into a towncar van hire to pick you up from your resort and take you to Universal, then pick you up at Universal at the end of the day and take you back to your Disney resort.
Florida Tours is popular here on this board and Tiffany Town Car is also a company we have used. Tiffany Towncar charges $70 RT for a van plus tip, Florida Tours charges $114 RT for a van plus tip.