Why are there four types of execution? Wouldn't it be enough if there were only one type of execution? Lashes for example are only of one type and the standard 40 lashes.
There are different types of execution to highlight the various severities of the sin for which the sinner is being executed for.
As the Rambam writes (הלכות סנהדרין פרק יד):
סקילה חמורה מן השריפה, ושריפה חמורה מן הסיף, והסיף חמור מן החנק.
"Stoning is more severe than burning, burning is more severe than beheading, beheading is more sever than strangulation."
Similarly there are various types of "heavenly killing", e.g. כרת, מיתה בידי שמים, ערירי depending on the severity of the crime.
There are also different types of Korbanot, depending on the sin.
Even in monetary restitution we find that sometimes you pay what you damaged/stole and sometimes you pay more (חצי נזק) and sometimes you pay more; double, 4 or 5 times, and sometimes you get fined.
I think we should start off with the very idea of punishment. As we all know, the Jewish approach is not to punish for the sake of punishment or even threaten the rest of the nation, but to give the sinner the atonement he deserves.
As we also know, a sin's harm is two-fold: it does a damage to the world as well as to the sinner. I learned that there are 3 levels of personal spiritual "damage" to reflect the severity of the transgression:
External (monetary): as person's possessions are his "outer self" (therefore the money is called דמים as blood), some "low-level" sins can be simply repaid.
Surface: lashes are given as a "skin-deep" punishment for a "higher-level" sins.
Internal: the capital punishment is given for the "high-level" sins.
The corporal punishment (as I remember from some Kabbalic books, a clear source needed) is further divided into four to reflect the type of damage according to the 4 constituent elements of the human body (traditionally): fire, air, water, and dust. So if the sin comes from a person's "spiritual fire" or "damages his fire part", the fix/atonement would be שריפה, if it was the air - that would be חנק, the others are סקילה for the dust and הרג for water (never realized why the last).
I admit, even if I understand the analogy I couldn't understand the division of the sins into those four, for example, "הבא על נערה המאורסה אינו חייב עד שתהא נערה תולה מאורסה, והיא בבית אביה. באו עליה שניים - הראשון בסקילה, והשני בחנק:"
NB As Danny noticed the Gemorrah (Sanh 50) tries to figure out the hierarchy of those four types also.