If we have a surplus of rubbish (say after Christmas or if we've hosted people here), I nip around the neighbours with space in their bins on bin day and ask if I can put any extra in their bin. I always manage to get rid of it all in one bin collection doing it that way. There are several neighbours who have said if there's space once they've put it out, to use it as they empty the indoor bins before they put their big bin out.
I assume if your rubbish bin has been emptied, it's recycling next collection. Will they take extra recycling where you are? Our council won't collect extra rubbish, but they will take extra recycling within reason.
If any of it is metal, there are plenty of people who will collect that from you for free as they can weigh it in for cash.
Might there be any bits from your son's room clear out that you can arrange for a charity to collect, or stick on Facebook etc for free?
Some types of wrapping paper are suitable for shredding for pet bedding. I've seen several local adverts asking for the plain kraft type wrap for this purpose, it might be worth a look if that's the type you have.
Once you can get any waste out of the house, it will look better, and hopefully feel less overwhelming. Never leave a room empty handed, and the clutter will deplete pretty quickly. Open the windows for a short while for a blast of fresh air, and it will start to feel better.