I think the main reason why you're being passed up is that your question is actually a lot vaguer than you probably think. The reason for this is that there's no such thing as the "Hellenic Period," which makes it difficult for users to figure out exactly what period you're talking about. So, I'll err on the side of caution and assume you're talking about every period.

I'm going to obviously leave out the Mycenaean Period and the Dark Age because we have no idea what was going on then, no matter what speculation we throw around. During the Archaic Period we get a slightly better picture, but we have no knowledge of any kind of organizational structure. It seems likely that during the Archaic Period local neighborhoods raised and organized troops within the levies, and that these forces operated together under some appointed or elected captain. Undoubtedly there was some sort of officer's organization, but we have no idea what it was (besides, of course, generals) or what the functions of each officer might have been.

During the Classical Period we start to get a decent picture. Starting around the middle of the 5th Century we start to hear about officers a bit more. Units were still largely divided up by locality and led by some member of the group, but officer positions like file-enders become known and are important. The main unit of organization in Classical and Archaic armies was the lochos. The lochos was a poorly-defined group of men, and could be just a small band or a large group several hundred in number. The reason for this, apart from any lack of standardization among cities, is that lochos doesn't really mean anything. A lochos can be roughly translated to a "party," which might mean anything really (for example, the "Band" in Sacred Band of Thebes is the word lochos within the phrase leros lochos). What is clear, however, is that the lochos, along with the systems of local recruitment, developed out of the tribal systems of the Dark Age and the early Archaic Period, which gave Greek armies their overriding structure for most of antiquity. Our only real classical description of a lochos is from Xenophon, who describes the organization of the Ten Thousand. Some scholars argue that the Ten Thousand must have been organized along very generally representative lines, but others argue that since the mercenaries were originally led by Lacedaemonian officers and were mainly made up of exiled and disenfranchised Spartiates the Ten Thousand must have been organized much more like the Spartan army than any other. Xenophon describes the Lacedaemonian forces as being comprised of lochoi of 640 men, made up of 4 pentekostyes of 160 men each, further subdivided into 4 enomotiai of 40. Those 40 men were probably further subdivided into files and half-files, with file-leaders and file-enders. The lochos made up half of a mora, of which there were 6 in the army.

However, Xenophon's detailed description of the Spartan army only applies to it within certain conditions. For one thing, this is the Spartiate army around 400, B.C. at its maximum manpower. The Spartans almost never fielded their entire force, and we know that levies were called according to age groups, with only the youngest group being levied except in dire circumstances. So normally the tactical units would be deployed in various fractional proportions. In addition, this is the Spartiate army alone. Xenophon says nothing about how the subjects or the allies organized their troops, although it's likely that many of them copied the Spartan system. Finally, the Spartan army went through a massive reorganization during the Peloponnesian War, when it was discovered that even the Spartiates were totally incapable of dealing with the type of warfare that the Athenians were waging. Attempting to streamline and organize their outdated forces the Lacedaemonians reorganized their tactical formations, their officer system (not really, it was still corrupt as hell), and introduced methods of recognition (such as the lambda on their shields, traditionally introduced around 425, the same time that Athenian marines were raiding Spartan camps at night or ambushing columns and wiping them out. Establishing identity became pretty important). We're not really sure what the organization was like before, but it seems likely that the mora was a later unit introduced in this reform, since the word does not appear before Xenophon.

Most cities didn't operate like this. A later source gives us alternate names for the lochos, but he may well be referring to the Macedonian army. This same source claims that files were organized as even and odd, as were the half-files. However, we're not sure what army he's talking about or even if it's classical. The term lochos, classically, is often used more or less synchronously with a file, or occasionally a half-file or a collection of a couple files.

As for classical cavalry, it's a bit confusing. Many scholars agree with Snodgrass, who argues that during the early Classical Period the hippeis, or knights, of most cities were not actually cavalry, but rode into battle and dismounted to fight in formation. There are a great deal of reasons to believe this, but it also seems that cities like Athens also had a small group of horsed scouts, who were not usually expected to participate in battle. By the Peloponnesian War, however, we find that the Athenians have a permanent force of 1000 cavalry, which by then had probably been taught combat on horseback, since they patrolled the walls and occasionally got involved in skirmishes with Boeotian cavalry raiders. However, we have little knowledge of their organization.

In the 4th Century we find that the Phalanx begins to become an organizational unit. Note that the term phalanx simply means a formation of infantry, and that the Phalanx (capital P) as a formation only exists as a specific thing after Epaminondas. Epaminondas reformed the Theban army, introducing larger gaps in the line (as opposed to the previous formations, where troops were tightly packed to protect each other), as well as adding formations like the Sacred Band. We're not really sure what his organization was, however. What is known is that there must have been some significant changes, since the Boeotian levies under Epaminondas were much larger than those in the past, and since Epaminondas introduced extremely deep formations that were ill-suited to the organization along files.

Of Macedonian armies we know quite a lot. The core of the Macedonian army was the Phalanx, which was also the most important position for an officer to be posted to. Philip, when a hostage at Thebes, observed Epaminondas' army carefully, and reorganized his forces on his return with the Thebans as his model. Philip's Phalanx consisted of 6 taxeis of 1500, each of 6 syntagmata of 256 men. Each *syntagma was composed of files of 16 men (a lochos), each of which had a file-leader and file-ender, as well as one in the center of the file. Aelian says that the commander of a syntagma took the front-right position (as was usual), and that in the rear each syntagma had a herald, a standard-bearer, a trumpeter, an officers' servant, and the ouragos, who seems basically to have been a formation-ender, keeping the formation coordinated and organized. The Hypaspists were divided into battalions (they are usually referred to as battalions in scholarship) called chiliarchies of 1000 men, of which there were three. It seems likely that the smaller organization of the Hypaspists followed that of the Phalanx.

Of the cavalry, the Macedonian formations were organized somewhat piecemeal. Taking over and only slightly restructuring the old aristocratic system where the barons led their households, Philip had to deal with some poor organization here. As with the light infantry, generally each national contingent had its own organization, and considering how large a baron's household might be Macedonian formations might not be well organized either. The Companions we know were divided into squadrons of 200, except for the Royal Guard which was a squadron of 300. The Companions were not of any standardized number, and often their formations varied greatly in size, particularly in the successor-states. We also know that the Thessalians, who were considered more or less the same as the Macedonians, were probably organized more or less the same way, although they often adopted different formations (the diamond formation, for example, was well known in antiquity as being a Thessalian invention). Some scholars argue that the Thessalians may have even been raised similarly to the Companions, since the influence of Parmenio among them was enormous, with one scholar even suggesting that Parmenio's bodyguard (a special squadron of Thessalians) was modeled on and organized to ape the Royal Squadron.