Oh, that's just awful.
I've not lived anywhere with roaches myself but I know they can be hard to get rid of. Those bug bombs you can buy at the store yourself might help but they won't solve anything unless they are done everywhere in the building at the same time (otherwise the bugs are smart enough to simply go downstairs and avoid your cloud of death smoke for 4 hours). You will need a professional exterminator/pest control company to come out and fumigate the whole place, top-to-bottom. They will also probably leave some longer-term bait/poison traps around so be sure that the landlord tells the service if you have any small children or house pets who so they can use the safest roach traps and place them in inaccessible spots (behind and underneath appliances/vents).
If you make it clear to the landlord that he needs to take care of it right away, he probably will do that rather than go through expensive legal hassles (but watch out if he says he called someone but you never get any notice that they are entering your unit or that you need to be out of the house while they do the fumigating since that might mean he just gave you the run around and didn't actually call anyone).
If he doesn't do anything about it, be proactive and take pictures of the infestation (try to turn on the lights in the middle of the night and then snap pics as they tend to come out in the dark). If you can't afford a lawyer call social service places (like your local United Way/First Call for Help) and get referrals to legal aid. Most places have free or low cost legal counsel available for housing related issues (you may have a tenant's union where you live too). Pressure from a lawyer might be needed later on. One mistake to not make: don't stop paying your rent on the basis of the infestation without seeking a lawyer and putting your rent into escrow. That step proves that you aren't just making up an excuse to avoid paying your rent when it's due (you essentially put the rent into the escrow account on time but deny it to your landlord until he performs his part of the lease agreement- by providing you a habitable, sanitary rental). Good luck!