Unless delivered by the postoffice, flyers are not permitted to be placed in mailboxes, pursuant to Postal Regulation. They can be left at your door or in a newspaper holder.
Strictly speaking, it is not legal to have material that is not actual postal mail, which is mail that has been stamped and processed by USPS, put into mailboxes. That should include flyers.
It is a federal offense to put anything other than postage paid mail in a mailbox. Call the advertisers and ask them to stop. The other thing you could do is put a no solicitation sign up in which case they are legally bound to not leave advertisements at your house.
It is illegal to put flyers in mailboxes. It is a violation of people's privacy. You can be charged for trespassing and tampering with federal mail if caught. These are very serious charges and have penalties of large fine amounts as well as prison terms in some states. A better solution is to mail them legally.
No, it is illegal for anything to be placed in a mailbox which has not been sent through the mail, with postage paid. If the postage has been paid and the item is properly addressed, it must be delivered to you.