This is a huge undertaking - especially if your kids haven't been trained to enjoy the car for hours on end.
And to boot, each kid has their own set of age-related challenges!
First off - unless your kids are already allowed some screen time, or are aware that they will be getting to watch movies, don't use that as your first option. Pack a portable DVD player or download some entertainment to your phone to watch offline and only use in case of emergency. (As in, you're stuck on the highway in the middle of a huge traffic jam with no escape for hours).
Plan as much of your travel as you can while the kids are asleep. Leave at 4AM each morning (seriously!) and stop to eat breakfast after the kids are up. Make sure you're on the road while at least one of your older kids is napping (if they nap, that is.)
There are a ton of relatively inexpensive car seat trays that are great for snacks and activities. Pack a small bag of activities for each day's travel (crayons, legos, etc) so that the kids have a 'new' activity to look forward to each day.
Your kids are going to get bored of it fast. Like real fast. Day 4 will likely be an absolute nightmare getting underway. By the end of the drive you will probably have tunnel vision for your destination.
DON'T TELL YOUR OLDER KID WHAT THE NEXT STOP IS GOING TO BE. It's better for them to be surprised at each stop than to be disappointed that an expected stop is no longer on the docket.
Are your older kids potty trained? Are they girls? If so, a portable toilet is a must. If they're boys, just pull over and let them go out the side of the van.
Become familiar with some of the dead zones (long stretches with few/sketchy stops in between) and make sure you devote your energy to moving through those areas as efficiently as possible. If you're not prepared that's where you'll inevitably need to take an emergency stop. Every time.
Since you have a flexible timeline, and going back up to my point above. I'd stretch each journey into at least 5 days (~2500 miles - 500 miles a day give or take). Leave 4-6am daily, drive 6 hours (with stops). Break for lunch. Drive 2-3 more hours (through naptime), stop for the day. Repeat 5x. Maybe even throw a day or three of no travel in there.
On the East Coast side of things, Memphis, Nashville, Asheville, Pittsburgh, Hershey, Philly are all really cool places for your journey there. On the way back, Niagara, Buffalo, Columbus, and Indy are all interesting in their own way.
I assume you've ruled out camping? If so, a lot of times you can score great deals on hotel rooms by booking last minute late in the day. Hotels will usually offer pretty substantial discounts if you book same day, near the end of the day, because an occupied room at a discount is better than unoccupied.
Sorry for the scattershot. I have 2 kids and we go on 8-10 hour drives probably 6 or 7 times a year. Plus, i grew up only having flown on family vacations exactly once.
As far as saving on lodging - I assume you've ruled out camping. If