savvy,
Schools may *say* that they want the LORs sent to them when they notify you, but you should disregard that statement. Send the LORs as soon as you possibly can to the schools. They are going to request them anyways, so there is no need to delay your application by a month waiting for schools to receive them after they request them.
Besides, if you are applying through AADSAS, they send your letters out at the same time they send out the application, if you choose to let them.
Have you already applied through AADSAS? If not, then I'd encourage you to have them send out your letters. That way the recs. only have to write one single letter, and AADSAS does all the copying and mailing.
You can have the recs. return their letters to you in a sealed envelope and then you can mail them out, or you can have your school mail them out if they have an application service.
Both of these latter options are going to be a bit time consuming for you, and annoying for the letter-writers (especially in light of the fact that you are applying to 20 schools). If you have 3 letters written, then you are going to be dealing with 60 copies of letters if you choose to do it all yourself! Too much of a pain for me.
To your original question: The teachers can mail the letters for you, but you need to provide them with stamped envelopes (they shouldn't have to pay for it --especially 20 schools each!).