Hi!

The short answer: Parts of East Frisia became part of the HRE at different times.

The long answer:

The lands called Frisia which may or may not be bounded by the north coast of modern-day Netherlands is a pretty hard land to rule over, which can be seen from the assassinations of several Margraves of Frisia in the 10th and 11th Century which included (and is not limited to) Henry of Northeim and Arnulf I. The end of the rules of the Margraves led to the so-called "Frisian Freedom" around the 12th-13th Century wherein local rich people called the Vetkopers (Fat Buyers) and the poor people called Skieringers/Schieringers (Speakers) were constantly feuding and running the place, according to contemporary Vetkoper Janko Douwama. [1] Essentially during this time they are de jure supposedly under the rule of the Margraves of Frisia which were considered vassal of the empire Charlemagne established but it is unclear whether they paid homage to the Holy Roman Empire, as established by Otto I. My personal take on it is probably not.

However, around 1460 the Habsburg emperor Frederick III wanted to integrate the free Frisian lands that had previously caused so much trouble by not only hosting at one point one of the largest pirate/privateer fleets of the (European) Middle Ages, the Victual Brothers, but also feuding with the Duke of Saxony. (no, not the Saxony near the Czech border but the Saxony near the North Sea) That tangent aside, Frederick III accepted fealty from and raised to the status of an Imperial Count a Vetkoper named Ulrich Cirksena in 1464, thereby de jure annexing the East Frisian towns of Aurich, Norden, and the then-small port town of Emden, plus a few noble estates near said towns. [2]

With the Lordship of Jever, their independence until the 14th Century was due to the prosperity of the town as a center of trade, though having the Victual Brothers as a guardian of the town's independence in return to providing them a safe port haven is a big boon. They became part of the HRE around the 14th Century only due to the extinction of the Wiemken dynasty with the death of Maria of Jever in 1575, and the lordship passed on to the Counts of Oldenburg via Maria's will. [2]

In conclusion, as East Frisia wasn't itself one entity most of the time (though at times it was one title) answering the question as to when East Frisia joined the HRE cannot be answered with one date alone.

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Sources:

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[1] Boeck der Partijen, Jancko Douwama

[2] Heart of Europe, Peter H Wilson

I will answer the Jever question. The history of the Lordship of Jever throughout it's existence until the annexation by the (Grand)Duchy Oldenburg in 1818 it's complicated. Your confusion stems from the fact that Jever was only incorporated in a Reichskreis (Imperial Circle) in 1548. The Circles were introduced in 1500 and by 1548, there were the Burgundian, Westphalian, Lower-Saxon, Upper-Saxon, Electoral-Rhenish, Franconian, Swabian, Bavarian and Austrian Circle. The circles' primary functions were of military nature and for the purpose of collecting taxes. But some regions weren't made part of the circles - for example Jever. The reason it was incorporated in 1548 - into the Burgundian circle, albeit it was geographically much nearer to the Lower Saxon circle - was that Lady Maria of Jever who ruled from 1517 to 1575, gave up the imperial immediacy and became a vasall of the Duchy of Brabant which was part of the Burgundian circle. That was preceded by a conflict with the neighbouring county of East Frisia: Maria only become the ruler after her brother Christopher died with 18. The more powerful count of East Frisia entforced a marriage contract for Maria with his son so he and his descendants would get the territory, but they already invaded before they married. Maria was held as a hostage until 1531. In this year, the East Frisian troops were driven out of Jeverland and Maria decided to sought the help of the Emperor. The emperor now guaranteed the independence of Jever from East Frisia, but in exchange he, as duke of Brabant and count of Holland, took possesion of the territory and immediatly giving it back to Maria as a fief. Because of this, Jever became part of the Burgundian circle and stayed there, even when it later changed into the possession (still as a fief and not immediate to the empire) of the count of Oldenburg (after the death of Count Anton Günther of Oldenburg in 1667 it changed into the possession of the Prince of Anhalt-Zerbst, later becoming Russian and in 1818 Oldenburg again).