Originally legates were ambassadors of senatorial rank, invested with special rights and privileges to conduct diplomatic actions outside of Italy. Legates quickly became mere advisors to more important, imperium-holding magistrates--the New Pauly suggests that this occurred by the late 3rd Century, B.C. This was their essential function throughout the remainder of the existence of the office, to serve as advisers and staff members for magistrates holding imperium and promagistrates. This could consist of purely administrative duties, or military command. I suspect you're asking about the latter. Legates granted military command became common during the late Republic, although the office of legatus legionis only became an official officer position during the Republic. Normally a legate would command a legion or two--the number of troops under his command was more or less at the whim of his superior and changed depending on the situation, although in the late Republic it tended to be one legion. However, legates could be granted propraetorian powers, which gave them legal power to command the same number of legions as a praetor (which I think is four, the same as a consular army). Unlike a regular legate, who only commanded for his promagisterial superior, a propraetorian legate held imperium in his own right, and could theoretically undertake actions independently--famously Caesar granted Labienus propraetorian status and let him campaign essentially independently for a season or so. The New Pauly notes that propraetorian legates as appointed by promagistrates are a feature only of the late Republic--they were unnecessary before Sulla's institution of propraetorian governorships, and Augustus made legate appointments official, imperial business.

There were several kinds of tribunes: military tribunes, tribunes of the treasury, tribunes of a cohort, of course the immensely powerful Tribune of the Plebs, etc. I suspect you're asking about military tribunes. Like all tribunes, military tribunes were elected by the Tribal Assembly (hence their name), and acted as military commanders under legates and promagistrates--in other words, they could not hold imperium. During the Punic Wars, each legion in a consular army contained six military tribunes, elected from different tribes, who commanded the legion in rotation--according to Livy, additional legions beyond the consular four that were raised had their military tribunes appointed by the consul. According to Polybius, military tribunes of the 2nd Century had to have prior military experience. However, by the late Republic the division of the office into senatorial military tribunes (tribuni militum laticlavii) and equestrian tribunes (tribuni militum angusticlavii) was pretty well-entrenched, and the senatorial tribunes tended to be more of a political office than a military one, providing some military experience (though not really that much--Caesar served as a military tribune in his youth but was considered more or less totally inexperienced in military affairs when he began his proconsulship in Gaul) and allowing a young politician to learn how to win an election. Equestrian tribunes technically couldn't command legions at all, and senatorial tribunes really just observed the legates and took orders from them every now and then, although they could command a legion in a pinch. Tacitus notes that by his day equestrian tribunes really weren't required to do anything, and commended Agricola for not slacking off and sitting on his ass like many young tribunes. Under the Principate military tribunates were restricted to high-born boys and served as the preliminary step to taking the cursus honorem.

Imperator is not an official position, at least not until Vespasian's lex de imperio. A magistrate holding imperium, after a successful battle, might be hailed as "imperator" by his troops. It was a sort of unofficial title that then allowed the man to add it to the end of his name when he wrote letters (at least during his term of office--once he crossed the pomerium a general gave up the title, along with his imperium) and being hailed as an imperator vastly increased a politician's dignitas and auctoritas. The New Pauly notes that while before Caesar magistrates were generally hailed as imperatores for specific victories (and would often list the number of times they won the title--Sulla, for example, did this), Caesar won so many important victories that it became redundant to count. Caesar also used the title within the pomerium (though he did hold the office of dictator for much of that time, and I'm not sure whether a dictator could be an imperator in the city--as I recall he retained his imperium within the city). It's important, though, that Caesar did not permanently affix it to his name, and only used it sometimes. Under Augustus and Tiberius the title was restricted to the imperial family, but was still only granted if a general was hailed imperator by his troops. Vespasian's lex de imperio permanently affixed the title to the emperor's name, and it essentially became an official magisterial office held exclusively by the emperor