tinker, I hate my house being an open house all the time.
Don't know if this would work for you but I get children to play and chat in the hall and front steps. I keep the front door open or on the latch, but am within hearing distance so would instantly know if someone comes into the living room or up the stairs. This means the house does not get taken over. I check who is on the step very regularly - and can get a good idea of what is going on by the noise or lack of it. I get uneasy if children I hardly know are in and out of all our rooms. If I have invited children inside properly, I tell them what rooms they can go in and stick to this. I never let them play in my sons' bedroom - don't want them thumping up and down the stairs and don't want any child saying to their parents I was in 'x's' bedroom and 'y' happened. OK very paranoid, but it's a rule I stick to unless the children are real friends of my sons and are on a proper playdate.
I aim to let my sons only play with one type of toy at a time, then put it away - they can fetch things from their room but no one is allowed up to choose with them. I like them to keep track of what's outside. I don''t let my sons take out certain small or expensive toys - my past is littered with stories of stolen pokemon cards and footballs and sadly, even the odd gameboy game. Also, toys end up getting mysteriously broken so I am very watchful if older children or children I don't know start playing with my sons' toys. I have no qualms about taking the toys in pronto if I feel uneasy. And that includes bikes and scooters - an older child messing around on my oldest son's bike a few years ago caused £40.00 worth of damage in 20 minutes. I usually don't let any children take turns on my sons bikes now. My oldest son is now wary about sharing his stuff anyway - he would never take his gamegboy outside for instance and let others take a turn. He has suffered too many losses and he knows we would not replace things that get stolen or broken.
I have no qualms about saying no to children coming inside. I just lie to them I am about to do lots of housework (!) so need a quiet house or I have a headache or something - we don't tend to do taking turns around here, but most children just play in each others front gardens or on the steps.
I never allow young children into the house unless they have told their parents where they are going. I don't want my youngest to ever feel this is acceptable. I don't want him thinking he can visit a friend's house without checking with me first. There are only 2 houses he can visit and they are very close to us.
Some of the older children (9 and over) say their parents don't care where they are in the street, and they are probably right but through painful trial and error I now never allow them inside to play anyway. They go on the front step.
I also think it's really important to keep a running check on who is in the playing out gang and make rules accordingly. Luckily for us, the playing out children were mostly nice, sensible girls, but recently two wilder boys aged nine or so have joined the gang (my oldest son doesn't like them) and I am not as happy. Still that's another thread subject...