As far as the other kids' parents go, maybe you can ask them to come over for a play date at the park or a bbq or something. Just say something along the lines of how nice it would be to get to know the parents of your kids' friends. That can be an eye opener sometimes. Or if you don't really want to do that, maybe you can just introduce yourself and ask about any allergies that they may have. You'd hate to give the kids a snack and for someone to have an allergy. Other than that I don't know how they can let the kids go to other people's home and not at the very least meeting the parents that live there.
As far as the kids go. I've had to be pretty frim w other neighborhood kids before. The first few times a "new" kid is over I ask all the the kids (mine and their friends) to sit down and put on their listening ears and I tell them That I have house rules that I expect to be followed and then I list them (use your words and be polite, share, when you're all done w something it must be put back were you found it and if you don't remember then please ask and to treat my home the way you would want someone to treat yours, if you don't like some one throwing your favorite toy or jumping on your bed at your home then please don't do it at ours.) That's usually my "speach" Short and sweet and to the point. And it helps if you ask the kids to repeat it to you, point to one and ask if they can tell you one of the rules if they don't answer then ask if anyone else knows. The kids will usually pay attention to each other a little bit more and also it seems to help them remember it they have to repeat it. Then I tell them to go have fun.
I check in on them ever once in awhile. When I check in on them I like to ask if they'd like some juice to drink or a snack. Most of the time they'll say yes and then you can ask them to pick up the toys while you get the snack. The kids seem to do a better job at getting the room picked up if they know they'll have a snack waiting on them instead of me just telling them to pick up.
If I notice kids fighting over a toy I give them a warning w a chance to work it out (I'll say something like -I know we aren't fighting over that. I'm sure you can work together and share and it would make me really sad if you can't because then I'll have to take it away and I know you guys don't want me to take toy do you?) And if I have to I put the toy in sight but out of reach. If it's in sight but out of reach then sometimes they'll come out and ask to play w it or for me to get it down for them and I'll tell them no and I'll ask why. If it was a kid that was not fighting over the toy then I'll tell them that I put it away because people were not sharing it. If it was one of the kids that where fighting over it then they'll usually answer 'because me and so and so did not share it' (or something like that) and then I'll tell them that that's right and maybe next time they'll do a better job at working together and sharing. All of this can be a pain in the neck sometimes but it's super helpful because it gives you the chance to have them think about the rules.
I've also gotten many "well, that's not how we do this and that at my house" type coments. To this I say as nice but as firmly as I can "I understand that your mom and day may do things differently at your home and if I were I your home then I would follow their rules. But at our home we do not do (what ever it is) and I would like if you followed the house rules at our home just like I would follow yours at your home." Most of the time just that does the trick but they're all sassy and not listening then give them fair waring that if they can not follow the house rules then they will not be allowed to come over and play. If their sibbling is behaving and listening then tell them that their sister/brother can are still welcomed because they are behaving.
And as far as always calling or ringing the bell if my kids can not play at that time I tell I will have my kids call or come get them. If my son is cleaning his room (or something) then I have had to tell a couple of kids before that the more they come ringing the bell or calling the longer it will take him to finish cleaning his room. When they give me they "what are you talking about" look I tell them that every time they come to the door you kid stops working and the more you child stops then the longer it takes for him to get the job done. I've also had to pretty frim in saying, that just because we are home does not always mean my kids can play we have other things to get done sometimes. Sometimes its been helpful if my kids come to the door/phone and tell their friends that they can't play right now themselves and that when they're done they'll call em. Also, sometimes my 6 yr old wants to get all whinny and cry about nearly everything (this just started about 4 months ago) and when he gets like that I make him "rest" (he usually ends up taking a short nap and then is all fine agian) but instead of telling his friends 'oh, he's napping right now' I tell them that he wasn't feeling well and wanted to rest for a little while and he'll call you when he's feeling better.
There has been one kid that I've had to do the 3 strikes and youre out thing w. He and my son will just start fighting sometimes. The 3rd time that i have to brake it up w them this kid gets sent home and they can't play together the rest of the day. That seems to be helping.
So, that's about everything that I have found that works for me. Hopefully you'll find something that will work for you.
Sorry I made this so long...
Good luck!