i never really understood the east germanics, they supposedly originated in Scandinavia
As constitued peoples, Eastern Germans were products (or rather by-products) of the Roman limes: while they certainly had elements coming from Poland and maybe Scandinavia, the idea that whole peoples migrated as such crossing all Europe before settling in western Romania is less historical than the result of heavy inspiration from best-sellers of the era on "origin stories" as Aeneid or Exodus.
Goths for instance, emerged as a distnct people likely along the limes as a mix of Germans (western and eastern, that took a great importance), Sarmatians, Dacians and even Romans in the IIIrd century.
but kept popping up in different seemingly random regions, Spain, Romania, Italy, North Africa, Crimea
As for Rumania and Crimea, it's basically the regions where such peoples began to emerge both institutionally and structurally.
As for Spain, Italy and North Africa, as
@Albert.Nik said, it's where these peoples (augmented by other elements, Barbarians or Romans) finally settled due to political context : Barbarians had a tradition of service in Romania, usually paid by subsides (coinage or supplies) and when this declined, and willing to both survive and maintain this prestigious and fructuous service they first went raiding, then (when the pressure was too big, and raiding less of a systematical option) entered Romania as whole peoples.
It could have stopped relatively early on depending on the situation (meaning foedi being mostly stuck to the limes, as it happened in late IVth to Vth for Franks) but eventually it didn't and we had groups settling in rich provinces eventally forming polities there.
then they just disappear into thin air a few centuries later ? Like what ?
It's essentially because Barbarians that entered Romania were products of Roman civilisation : they appeared from a social-political elaboration fed on Roman trade (mostly wealth, but mettalurgy as well), subsides (supply or gold, which was decisive into creating a social-political mobilisation), and general influence since the Ist century AD.
You simply don't live next to the great political and cultural behemoth of the era without consequences (consersely, it meant provincial Romans, due to this relations and settled Barbarians in Romania since the Ist century (such as in Gaul or even Italy) recieved some Barbarian influences (not even remotely close to the degree of romanisation of Barbarians this being said).
All these peoples emerging on the limes from a lot of various elements (and while in some eastern Germanic elements may have played an important role, it was far from systematical : Burgundians and Lombards for instance, probably spoke a western Germanic speech) were eventually importantly under Roman influence to begin with. Furthermore, still depending on their relation with the Roman state and institutions, they got integrated within its frames and instituions (regardless of the will of the Roman state to do just that or not) as foedi, mercenaries or even (as Romans of Barbarian origin) as playing a major role into the Roman state. All of this, integrating more and more Roman cultures, and Roman groups within them, meant that by the Vth century, the best way to differenciate a Barbarian from a Roman was political : if someone served a Barbarian king and not directly the Roman state,there was a chance he was Barbarian. In term of material culture, the difference is almost inexistant.
Now, by the late Vth and VIth century, there was the problem of what defined a Barbarian now the western Roman state was declining then gone, Barbarians and Romans being more and more difficult to distinguish (especially as Barbarian state inherited the Roman state structures), there was a lot of various identitarians elements that were put forward.
As their languages were largely out of use by the VIth century, it was kept into some ceremonial use (to the point Gothic writers sometimes attempted preposterous mistakes in latin to say "we're totally Goths, we do not take candle...Does it works?"; specific material culture (such as fransiscae, which were definitely absent before the VIth among Franks, but borrowed from peoples living further in Barbaricum, taking as granted they were Barbarians so so they were themselves).
Religion played a role too, Homoeianism being considered as a good marker of what made a Barbarian (Burgundians even switching from Nicean to Homoeian Christianity in the IVth), Law codes such as Alaric's or Salian (which are basically rebranded Roman laws on Barbarans) and even clothes (basically bling).
More important maybe, they elaborated their own history : Romans scholars considered that only real peoples had ones (Greeks, maybe Persians, Egyptians? and with Christianisation Hebrews) and that the others were kinda in a stasis (Romans, and Barbarians eventually, keeping taking Tacitus' account as granted for the Vth century). So, taking inspiration into ethnographic models found in the Bible (specifically Exodus) and Aeneid, Barbarians went to create a fanfiction about themselves in a romanized conceptual world. They mixed possibly with some remembrances on their actual history (Cassiodorus' account of the Scandinavian origin of Goths, which probably match the origin of some elements that formed Goths eventually in the IIIrd century)or pre-Christian beliefs (such as the fantastical elements in the story of Merovee) but generally it's about how they met everyone famous in the past (mythological or not), and erred in the Barbaricum founding totally real Great Empires (they just happen to live in Canada) before settling in a land that waited only them.
As identitarian differenciation goes, it was more efficient in bulding a broad identity rather than to differenciate with Romans : by the VIth/VIIt century, northern Gaul's population overwhelmingly defined itself as Roman, Spain was called "Gothia", and so on.
The prestige and material benefits of integrating a Barbarian identity was simply too obvious, and the deep Romanization of these peoples too great to make them other than Romans playing Barbarians after a while.
Did they move tens of thousands of people at a time ?
Vandals, a major group, were said to have accounted for 80 000 persons crossing to Africa, counting virtually anyone including slaves, women, childs, i'm-no-dead old peoples; on which a bit more than an half were able to fight (hinting at the importantly militarisation of these peoples). It's both significant, and possibly pointing on ammassing a lot of groups along the way.