Strictly from a medical/physiological standpoint, there is no real way to "overwork" your genitals with too many orgasms. Overworking your EXTERIOR sexual organs is a real possibility (for example a rash or soreness from friction on your shaft) during extended sessions, but is not generally hazardous to your health, and is a topic for a different discussion.

As for your internal sex organs, there's not really too much that you can do to damage or "overwork" them, strictly from extended sex sessions, or multiple ejaculations. They way that your sexual organs work, is that semen and seminal fluid (provides nutrients, lubrication, etc.. to sperm) is produced and stored in your testicles. Your body is continuously creating new/fresh sperm and seminal fluid at a reasonable rate, and absorbing old/dead sperm. This sperm and seminal fluid only constitutes part of your ejaculate though. The other part (which accounts for about 1/3 of your ejaculate), is fluid that is manufactured and stored in the prostate. The prostate is a small gland (about the size of a walnut), that surrounds the urethra (the tube that carries urine from your bladder, and other fluids out of the penis). It is a very sensitive organ, that is most easily accessed via the anus, and one of the reasons many men enjoy anal play (including myself). The prostate (like the testicles) continually produces a fluid (commonly known as "prostatic fluid") important for reproductive abilities (such as neutralizing the acidity of the vaginal tract allowing the sperm ejaculated to survive longer), and stores it until needed. When you ejaculate, your prostate undergoes strong muscle contractions and begins to secrete its fluid into the urethra, as the sperm from your testicles travel through the epididymis, up the vas deferens, and through the ejaculatory duct to mix with the prostatic fluid in the urethra. These fluids combined, due to the muscular contractions are expelled from your body as ejaculate.

On your first orgasm, everything is normal, and you body has muscle contractions that will expel a good portion of these fluids (but not all of it). For extended periods of sexual play, leading to multiple orgasms and ejaculations, your body will just continue to undergo the muscular contractions that force these fluids (or what smaller amounts of them remain) from you. This is why a second or third ejaculation in one session will always produce a smaller volume of ejaculate. Now, due to the rate that your body PRODUCES its sperm, seminal fluid, and prostatic fluid, if you are undergoing these multiple ejaculations in a single session (of a relatively short time frame), it is possible for your body to expel as much of these fluids as it can get out of these organs, before it has time to produce enough more to cause anything to come out of your urethra during further muscle contractions. This is what AveryDragon was talking about, and is known to many as a "Dry Orgasm." Your body is still reaching the point of orgasm, and undergoing all the pleasurable muscle contractions, but your body hasn't produced enough fluid yet, for anything else to come out. It is not harmful to you, but as has been mentioned, when you do ejaculate this much, you can feel a dull "soreness" in your groin from the repeated, numerous muscle contractions that your body isn't used to.

Your body will continue to produce it's fluids, and after some time away from sex and ejaculation, your glands will be filled back up, and ready to ejaculate again, completely as normal. In fact, if you were ever curious, this same system is what causes "wet dreams." When your body continues to produce so many fluids that it fills up the organs, and they aren't released by an ejaculation, your body will eventually need to "flush the system" to prevent old cells and fluids from "going bad," so it will trigger the muscle response to release them (usually in your sleep). I guess reaching dry orgasms is sort of the opposite end of the spectrum from there.

Does this make sense to you? Hopefully it clears up some of the confusion, and gives you a bit more understanding into your body and the way it works.