With examples from Stargate.
To begin with, let's define "slay." The word has two main meanings:
1. To kill violently. This is a formal and archaic definition.Example: Ba'al's First Prime vowed to slay all who attempted to thwart his master.
2. To overwhelm with amusement. This is the slang form.Example: "Yes, Colonel, your grade school pranks just slay me," said Rodney sarcastically.
The reason I defined "slay" is because which word you use for other tenses may be dependent on which definition you're using.
There are two words for the simple past tense form of "slay."
1. Slew - this word is mostly associated with the formal version of "slay."Example: "In years past I slew many fellow Jaffa," said Teal'c. "I will spend my life atoning for it."
2. Slayed - this word is mostly associated with the slang form of "slay."Example: Lorne slayed the expedition with his stand-up routine at the First Annual Atlantis Talent Show.
"Slayed" and "slew" can be seen as interchangeable, but it is still considered nonstandard for "slayed" to be used as the past tense of "slay" in the sense of killing violently. This is changing, however, mostly in the US. In the UK "slayed" is rarely used as the past tense form of "slay."
A quick note on "slew": It also has other definitions that are not related to the verb "to slay." "Slew" can refer to a large number of something. It can also mean to skid or move something sideways.
Example: TJ searched through the slew of cases that had been thrown haphazardly through the gate, hoping to find medical supplies.
If we're talking about the past participle and past perfect tenses, there are again two words that can be used.
1. Slain - Again, this word is more commonly used with the formal sense of "slay."Example: Scott had no idea how many of the aliens he had slain; all he knew was that he had to keep shooting.
2. Slayed - Oh look, this one showed up again. The "rules" are similar to the above: this form is mostly used in the slang sense.
As you can see, there aren't clear-cut rules. If you want to cover your bases, though, it's probably best to use "slayed" when you mean the slang term and one of the other past tense forms if you're really talking about someone being violently killed.