They are supposed to go to the post office and file a forwarding address form so you won't see their mail.
They might be doing this so bill collectors won't find them.
My solution wll take you an hour of work for the next two weeks but it will stop your problem.
1. The junk mail, coupons, etc., are yours if you want to use them, or put them in your recycle bin.
2. The first class and important looking mail:
Neatly type the word "Moved" on each piece and leave it in your mail box or give it to your mail carrier. If you leave it in your mail box put it in their so it stands out so the mail carrier knows you didn't just forget to get your mail yesterday.
Type the word "MOVED" in really really big letters above the address. Draw a line thru your address, in such a way that they can still read it. Your goal here is to make sure they don't re-deliver the mail tomorrow. But the post office needs to see what your address is, so don't block it out with a bold magic marker.
If you live in an area were your mail is delivered to a little box near your house instead of to your door, drop those pieces of first class mail into the out bound mail box.
In about a week, or two at the most, the post office will get the hint and stop delieving mail addressed to these other people.
The post office will then put the names of these people into their computer, along with your address and the computer which sorts the mail, when it finds THEIR name and YOUR address will mark the mail "RETURN TO SENDER" and you'll never see it again.
Another option is to save their first class mail for two weeks like you've been doing but keep the bag inside your house and then bring it yourself over to your local post office and explain to a clerk what you just explained to me and they will take care of it for you.
This way your hand writing does not appear on any of those envelopes.
If they still come knocking at your door, just tell them that for some reason, nothing else for you is being delivered.
If they harasss you after this you might need to call 911 and have the police tell them they cannot come back to your house looking for their mail anymore.
Technically speaking what they are doing is tresspassing.
Its one thing for people to do this for a few weeks until the post office implements the forwarding request that they filed.
It sounds to me like these people don't want those sending them mail to know what their new address is.
I moved two years ago and got a new phone number and I still get collection agencies calling me looking for the guy who had my current phone number before I had it.
The first three months it happened three or four times a day, now its down to about once a week.