If you need to send a package, and it fits the general weight/size specs of a book or CDs or video tapes, etc., you can use the United States Postal Service's Media Mail rate, which is considerably less expensive than standard shipping rates. Just remember that the USPS is getting wise to people abusing Media Mail (such as sending items that aren't books or recordings, or adding personal correspondence with an item), so they're "inspecting" packages that are sent that way. If the package is in violation, it will either be sent back to you, or will be bumped up to another higher rate, usually First Class, and the addressee (whoever is supposed to get the package) will have to pay the outstanding postage before they can receive it. If you don't know what qualifies as "Media Mail", go to the Post Office and ask, or check their website. If you need to send a letter with the package, use a clear Packing List/Invoice Envelope. You can get a box of these at an office supply store. Write your letter, fold it up, and write the address where the package is to be delivered on a small piece of paper (or a blank part of the letter) facing out, and slap it on the package. Remember that nearly all Media Mail packages go by ground, which means that anything sent to Hawaii or any outlying islands (Guam, Puerto Rico, etc.) will go by boat, which can take up to TWO MONTHS to get there! So you might want to consider sending things Parcel Post or First Class if it has to go that far.
Library Mail is similar to Media Mail. You can send packages up to 70 lbs at a very low rate (around $8 for a 20 lb. package), but they must be sent either to or from a "school, college, university, public library, museum, herbarium, or a nonprofit religious, educational, scientific, charitable, agricultural, labor, veterans, or fraternal organization or association." It's very useful for shipping your stuff to or from college - or form your own fraternal organization and make everyone you mail stuff to a member. The catch is that you can only send things like books, sound recordings and museum specimens - and ONE sealed envelope or a postcard. Like Media Mail, Library Mail is subject to inspection and general hassling. If you want to send anything other than books, etc, make sure the package is heavy enough to feel like a box of books, and then wrap it up tight enough that the post office won't want to bother trying to open it.
Priority Mail - Flat Rate
The USPS offers Flat Rate envelopes and boxes for their Priority Mail service (Anywhere in the world up to 3 days). If you can fit the item(s) in the envelope or box (provided for free at your local Post Office) and seal the flap shut, you can send it via Priority Mail. There are weight limits (4 pounds for envelopes and 20 pounds for boxes), but if you're sending lots of little items to one address, this is a real money saver. Just remember that shipping overseas will be more expensive than within the USA, but still, it's a good buy. Don't confuse this with Express Mail, an overnight service, which is more expensive.
A way to send mail without giving away your location by the postmark is to address a letter or package to the postmaster of the city you want the letter to appear to come from. Inside the envelope have your properly addressed and stamped envelope with the letter. The postmaster is required to open the first letter and remail the one inside untouched. Will the postmaster open it illegally or document the source post office, who knows?
Post Office Services
General Delivery, known in some countries as "Poste Restante", French for "post that remains", is a great choice for you if to the home carrier service or a PO Box is not an option. Your mail will be held at a Main Post Office for up to 30 days and can be picked up at any retail window. This is the easiest starter option if you don't have a permanent address. In the US the zip+4 code 9999 means General Delivery. The only real pain is if you have a long schlep to a main (full size) post office. Here is an example of how to address General Delivery in the US:
Mr. Abbie Hoffman General Delivery Washington DC 20090-9999
This address format is used in the UK:
Mr. Guy Fawkes Poste Restante Islington Post Office 116 Upper Street Islington London N1 1AE
This address format is used in Canada:
Ms. Pearl Taylor Hart GD STN A Calgary AB T0H 1A0
This address format is used in Australia:
Mr. Ned Kelly c/o Poste Restante G.P.O. Sydney, NSW 2000
This address format is used in New Zealand:
Mr. James Mckenzie Poste Restante Levin 5150
One of the difficulties with getting social services when homeless is that you have no proper mailbox to use when applying for aid. In 1994, the Postal Service issued a ruling that the homeless are eligible for a PO Box if they can provide a piece of official identification, a way to be reached, or proof that the postmaster knows them. The rule also declared that homeless people are entitled to general delivery service indefinitely, not for just 30 days. Unfortunately in some locations the US Postal Service has done everything it can to deny postal service to the homeless person.
If you are going to try to mail cash or packages to General Delivery/Poste Restante at a post office, wrap two or three large bills in a layer or two of newspaper, mail from a drop box, split the load into many envelopes over time if possible in case some get intercepted and stolen or confiscated. Other items and packages can also be sent in this way. Check with the local postmaster where you are for specific addressing rules.
You could try applying at the post office for a PO Box with your pre-eviction address before you get the kicked out, use the address of a homeless advocacy agency with their permission, or the address of a friend. Once you have the PO Box you don't really need to worry about the street address unless the they ask for updated information. An added benefit to having a real PO BOX is that in some offices you receive an after hours code to the heated mailbox room, which is of course locked so the homeless won't sleep there.