I found 6 to be a hard age with my dd, who only has one little brother, I'm sure having 3 little siblings is intensifying things too- but here are some of my suggestions:
1. Turn anything you can into a game, or race. "Can you get dressed before I can get socks on all the babies?" or "Can you take your toy to your room before I can count to 5?" Let him win these little contests, but not by much. We also made games out of a lot of other chores, like it was a secret mission to take laundry to the bedroom, or bottles out to recycle.
2. Give choices even when you don't want to- like "We HAVE to leave the house in 5 minutes, you can get dressed, or you can go in your pj's but I have to leave". That's an extreem example, but I've had to do that one.
3. Don't ask too much at once- I found my dd responds much better when only asked to do one thing at a time, rather than a list. Even if the list is "Get on your pj's, brush your teeth, pick a book for bedtime"- its too many things strung together and is overwhelming.
4. Spend time talking through problem solving what to do when the younger siblings do something. For example- my 2 year old will hit my oldest, but I don't want her to hit him back, so we had to talk through ways for her to respond that were acceptable. The solution my dd came up with is to take away what ever he hit her with- block, book, or to hold his hand if he used a fist and not let him move it a minute. We've had to talk through a lot of things about what is reasonable to expect of her brother, how exactly to deal with a 2 year old isn't easy for most adults, kids need a lot of guidance to figure it out.
I would also try to see to it that your son is getting some one on one time with you and/or dh without all the siblings- knowing how much attention my 2 year old takes, I can't really imagine having 3 that age and also needing to give attention to the oldest.
Laura, Mama to Mya 7/02, Ian 6/07 and Anna 8/09