Abarim Publications' online Biblical Hebrew Dictionary
The two forms תלה and תלא are basically two different versions of the same verb, which primarily conveys hanging something for conspicuous display:
The verb תלא (tala') occurs only in 2 Samuel 21:12 (conspicuously displaying of the remains of Saul and Jonathan) and Deuteronomy 28:66 (one's own life hung on conspicuous display). This verb also appears to occur in Hosea 11:7, in the difficult statement "My people are hung on backsliding...". This verb is either a plain Hebrew variant of the next verb or it is an Aramaic version of it.
The verb תלה (tala) also means to hang or display conspicuously and occurs all over the Semitic language spectrum. It's used for totems and regalia (Isaiah 22:24), common use vessels (Ezekiel 15:3), protective or ornamental armor (Song of Solomon 4:4, Ezekiel 27:10), harps on willows (Psalm 137:2) or the earth on nothing (Job 26:7).
But our verb is also quite often used for people who found themselves accursed, subsequently executed and finally publically displayed (2 Samuel 21:12, Joshua 8:29, 10:26). This display occurred mostly on trees since trees are excellent natural bill boards, which led to the general rule that whoever hung on a tree probably did that because he was accursed (Deuteronomy 21:22-23, Galatians 3:13; and "cursed who hangs on a tree" has nothing to do with the tree or with any magical or imprecatory powers attributed to the tree; hanging from a tree was the result of being accursed, not the cause of it).
Execution by hanging does not seem to have happened in the Hebrew world, but it did in Egypt (Genesis 40:22), Persia (Esther 2:23) and the Roman empire (Matthew 27:35). This old world hanging was usually a form of impalement and was not designed to break one's neck or choke one to death relatively speedily but rather to torture and display the victim at length as a deterrent. The Babylonians appear to have hung people by their hands, which would lead to death by asphyxia, as does crucifixion (Lamentations 5:12).
The only Biblical character who was clearly first hanged (or rather: hung) and then killed was Absalom, the son of king David (2 Samuel 18:9), but his hanging was accidental and not part of a deliberate procedure. It was, nevertheless, a fully functioning sign of disgrace, which would probably translate to modern imagery as some bad guy being killed while sitting on the toilet.
This verb's only derivative is the masculine noun תלי (teli), which is thought to denote a quiver (a case for holding arrows), but this is dubious. It occurs only in Genesis 27:3, as part of Esau's hunting gear, together with the words כלי (keli), a very common word, in this case denoting general gear (get your "stuff"), and קשת (qeshet), meaning bow, and this word occurs seventy-seven times.
Our noun תלי (teli) is thought to mean quiver because it's mentioned close to the word for bow, and also because quivers are known to hang. But it seems strange that our word does not occur elsewhere, and this while a handy quiver would seem more essential in a combat situation (which is where all the other occurrences of the word for bow appear) than in a hunting situation. Furthermore, just because we moderns speak of bow-and-arrows doesn't mean that the ancients did too. In fact, it seems logical that the word for bow covered not just the bow but rather the whole of archery equipment, including arrows and quivers (like our word "gun" denotes guns-and-bullets).
But the main objection against interpreting the noun תלי (teli) with quiver is that our verb תלה (tala) doesn't simply mean to hang, but rather to display something conspicuously. Even if the ancients would name a quiver after its hanging from an archer's belt (in stead of its holding arrows, which is its far more primary function and thus more prone to attract naming) they would have used a verb that simply means to hang, such as סרח (sarah) or דלל (dalal).
It seems much more likely that the תלי (teli) was not a quiver but rather an item particular to hunting, and here at Abarim Publications we guess that it may have had to do with the spreading out of an animal's skin in order to dry and preserve it; perhaps a clamp of sorts or a set of pegs and strings.