Book people or bananas (their even-cheaper end of line store) for books for party bag. Alternatively £1 bouncy balls, footballs, hoops etc all go down well. I've just spotted some 50p silicon watches on the sportsdirect site which I'm thinking of for ds1's party bag next month (having previously done the books and bouncy balls)
Keeping an eye out for suitable things in the sale - and then putting a note in your diary (for party time rather than when you buy them!) of what you have and where you've hidden them so you don't end up last thing at night tearing the place down looking for them the night before the party.
Activities that can turn into party gifts also work well - fabric paints and cheap cotton book bags or cheap White tshirts.
eBay is often a great source of really cheap party and party bag supplies but don't automatically assume it will be the cheapest.
If you're having problems getting parents to reply, get your dc to tell their child(ren) that you are sorting out party bags and will only make them up for the people that have responded. Amazing how the thought of no party bag seems to concentrate the child's mind and focus the pester power to getting the patent to ring you. Especially if you provide a printed note with your contact details on in case they don't have them to hand or have lost them.
3-4 year olds you're probably going to want the parents to stay (may well be 2 yr olds and several that aren't toilet trained so you're not going to want to start having to start changing somebody else's child just when you are supposed to be doing the games or tea or having a large glass of wine cup of coffee
5-6 yr olds may well want to stay behind without parents - make sure you have a list of children attending, column with their parent's name(s) in and a space for a contact number. Pre-fill if you have one but leave space for another one too. Don't let any child in or parent go without getting their contact details - and any allergies or other comments (eg veggie) in the final column.
If you're doing parties at soft play or other such venues that have multiple groups through for a meal, check that you really do have just your guests there for a meal. Especially in Reception or in a new school - it was only when we looked at the photos afterwards of ds1's party and asked 'who's that?' that we discovered nobody knew who she was. Still not sure if she was in the wrong party or did it regularly for a free meal on a Saturday!