I suggest that you try SuperNanny's routine. Go thru your usual getting ready for bed routine. Once they're in bed, lights out there is no more anything. When they get up put them immediately back to bed. The first time you can say, it's time for bed or some simple calm but firm statement. After that when they get up immediately put them back to bed without saying anything. Stay as calm as possible. Make it matter of fact. Assume they will stay in bed but be prepared to repeat this several times the first night and perhaps again the second night. By then they should've learned that bed is the only thing that will happen and they'll stay there. It may take a third night for some kids.
One reason that this works is that the child has no other choice. It's either stay in bed or immediately be put back in bed. If they cry or scream, ignore them. The only attention you give them is to calmly, quietly, without emotion putting them back to bed. Yes, the screaming may bother the neighbor but this will not go on for more than 2-3 days. I predict the screaming will stop almost immediately if you do not pay attention to it.
I also suggest, that even tho it's difficult, that you get them up at 7 or their usual time. Keep them on a sleep schedule until you get his problem resolved.
If they're continuing to take naps you could try keeping them awake so that they will be more tired by bedtime.
My grandchildren had difficulty getting to sleep at that age and their mother started putting quiet music or a book on CD on in their room and this helped. Five years later they still ask for the music or the story.
I suspect that you'll need to stop the current cycle of them doing whatever they can to stay up by using the immediately back to bed routine first or in combination with quiet music or a book on CD.
For me one of the hardest part of parenting has been acting as if I'm in charge even when I'm feeling frustrated and a bit out of control because my child/grandchild isn't co-operating. In charge means being quiet, firm, and consistent. It means taking action instead of making threats. It means not letting them know I'm at my wits end. In this type of situation it meant for me to focus only on the one task of putting them back in bed. I tend to move quickly to my next task such as doing the dishes, picking up the house or settling in on the couch for a rest before bed.
When I'm wanting to do something different than seeing that they're in bed I become frustrated much quicker and it shows. Kids pick up on that and continue to force my attention on them by asking for one more thing, getting out of bed, etc. But if you've given them adequate attention with a bedtime routine that's all that they need. Towards that end, be sure that you are focused on them while you're helping them get ready for bed. It's easy to get side tracked which can start the "one more thing."