I don't have a lot of experience, but I would strongly caution against going in the off season. In fact, the off season changes from year-to-year, so you need to be aware of show and parade schedules for the time you want to go. In 2005 they were running the summer schedule at the end of May. In 2009 the summer schedule didn't start until mid-June. I was very disappointed to find out that we weren't going to get to see shows...or even fireworks...during our visit.
As far as cost, we were in CA for five days...3.5 days at
Disneyland Resort...and the total cost including plane fare, a day's car rental, our hotel, and park tickets...was about $1200.
My cheap tips: As others say, use the HoJo's Entertainment rate. Use Supershuttle...the Entertainment book usually has coupons for them, too. Contact both the Anaheim and Orange County Visitor's Centers. They may have coupon books to send you...and the Anaheim site had printable coupons. Things like 20% off at the McDonalds there on Harbor. Every little bit helps!
If you stay at HoJo's you'll have a fridge in your room. With small kids, you should be able to have them share a suitcase, and take your fourth suitcase with food from home. I take cereal, breakfast bars, summer sausage and cheese that can be left unrefrigerated during the travel time, cream of wheat and dry soups that can be reconstituted with hot water from the coffee pot, crackers, individual peanutbutter packets, juice boxes, and things like plastic utensils, cups, and bowls. On one trip I took aseptically packaged milk and bottled Carnation breakfast drinks. If you stay at HoJo's you can buy fresh fruit, yogurt, milk, etc. in their little shop. We ate breakfast in our room every day except the day we went to Goofy's.
If you aren't a member of Mimi's e-club, join it about 2 weeks before your trip. You'll get a coupon for a free appetizer...or, you did when we went the first time. Watch Mimi's for other sales that may be going on during your trip.
Check the websites for the restaurants at Downtown Disney. We got a great deal at the ESPN Zone when we went in 2005.
Also, when in the parks, know that ice water is free. I control costs by insisting that my kids have no more than one soda a day while we're in the parks. Not only is it healthier, at the crazy cost for soda, if you have soda twice a day it will cost your family nearly $50!
Finally, give each kiddo a Disney gift card to be used for their souvenirs of choice. My kids know I'll buy them a pair of ears each trip. I've always bought them a t-shirt each, too. After that, they have to spend their own money. I also make the rule that they can't buy anything on the first day of the trip. That way they have a chance to know what's out there and make an informed choice. I've been surprised at what they've chosen. Their takes have included a Peter Pan bow and arrow set, a pirate sword, popcorn, charms for a necklace, and a CD of park music. My kids never bug me for "stuff", and I know ahead of time how much we'll be spending on souvenirs!