Offsite is definitely the way to go for a family of that size. You're going to want to have areas where you can gather together as well as places to go for privacy and time away from each other.
Here's an example of the kind of vacation home that you can expect to find in the Orlando area:
http://www.storytimeorlandorental.com/index.html
Both houses sleeps 14 and the rate on these 6-bedroom homes runs $240/night during "high season". You will not be able to find onsite accommodations for 15 people for that kind of rate! And there are many, many properties in the Kissimmee and Lake Buena Vista area that are just like this one. So do a web search and check them out.
For tickets, there's the "Give a Day, Get a Day" promotion, which would get everyone over the age of 6 the opportunity to get a 1-day/1-park ticket for free in exchange for a day of volunteer service. Check out the details here:
http://disneyparks.disney.go.com/di...ebrate/index?name=Give-A-Day-Get-A-Disney-Day
The nice thing about these tickets is that they are upgradeable to any number of days that you wish to add. So you basically get an $84 discount off of all adult multiday passes and $72 off of all the children's multiday passes. You cannot get that kind of a discount from the ticket resellers.
In order to qualify for free parking and some dining discounts, you might want to consider buying APs for a couple of the adults in the group instead of multiday passes. The above-mentioned "Give a Day" pass can also be upgraded to an AP. Check here for a list of AP discounts and benefits:
http://www.wdwinfo.com/discounts/discounts-ap.htm#general
Feeding a crowd like that is going to be a challenge. Having a full kitchen will help to keep the costs within reason. Plan to do breakfast at the house every morning. I would also make it a point to also do dinner there as much as possible even if it's frozen lasagna instead of homemade. Bring snacks into the parks to fend off hunger while waiting in long lines and have everyone carry their own refillable water bottle to stay hydrated. Fill them at the water fountains or get a cup of free ice water at one of the counter service restaurants. Packing lunches will help with the cost of dining but you can also share some CS meals between family members.
One final note about traveling as a group: Sometimes it's not a bad idea to split up every once in a while. It can be a nightmare trying to keep a large group together all day, especially when the ages vary as much as those in your group. You might want to make touring plans that include 2 or 3 groups going their own way and then meeting up at a predetermined location for parades or a meal.