The same way you investigate anything else, really. Look for corroborating evidence. Oral history alone basically proves nothing. So you look for documentation (the more contemporary, the better), or archaeological evidence, or anything like that.

This is true even when talking about eyewitness accounts, rather than stories passed down through generations. Take the example of video testimony given by Holocaust survivors. Often it was recorded a few decades after the events that happened, and it is very, very common for aspects of the testimony to be flat-out wrong. They'll contradict themselves, or remember events that we know did not happen. Human memory is very fallible, and any trained historian will know to keep that in mind.

But this is not to dismiss the value of oral histories, however old they are. There is a great deal to be learned from them, even when verification is completely impossible. Going back to Holocaust testimonies; for many portions of the testimony, verification is simply not a possibility, for any number of reasons. Say the survivor is describing an even where he or she was the only one to survive (which is common enough). Even without proof, we know a great deal about the type of events that occurred during the Holocaust, and we can know whether what they are describing is typical or not.

Finally, translation: it is always, ALWAYS preferable for historians to look at sources in their original language. I guarantee you that at some point in their careers, every single historian has cursed their stupidity in choosing to study a subject in a language that's not their native one. Take the Holocaust. If you want to study the Holocaust from the perspective of Jewish history, you need at a bare minimum to know Hebrew, Yiddish, and German, and probably at least one more language (Polish, Russian, Hungarian, etc) depending on what precisely you're studying.

I can only really speak for the methodology used in pre-colonial African history, I've never studied any other oral societies. There may be differences but I imagine a lot will be the same. When dealing with Oral histories, historians will obviously always keep in mind the same source related factors that one would bear in mind when dealing with most sources. Questions like: why was this history recorded? Who recorded it? Who had and and who has a vested interest in the propagation of this history? No historian is going to simply take any primary source at face value. Furthermore, Oral histories are rarely used alone, just as one wouldn't base a research paper from a single written source, one wouldn't base a paper on a single oral tradition.

When recording an oral history Historians will rarely take one persons oral history down and leave it at that. Most of the time the historian will travel around various settlements and take down as many oral histories as possible from as many different people as possible. Then, the historian will attempt to synthesize the oral histories to create a reasonable narrative for events. The official royal oral history of the Bemba for example is very different to that of the Bisa, a people whom were conquered by the Bemba in the early 19th century. By looking at as many angles as possible a historian can hope to get as close to the truth as possible.

As for verification, the most common thing to do is to try and verify the history against early written sources. Explorers journals, the journals of traders, travel diaries for example can all be used to verify where or not something happened or whether or not someone existed. For example when constructing a genealogy for a state from an oral history a historian might go through all available travel diaries for the names of the kings of an area. You might only find one per journal, but it would mean that you can verify that these people did exist and the genealogy constructed from the Oral history is true.

Alongside early written examples, historians will sometimes use archaeological evidence. Archaeological sights can often confirm a wide variety of things from simply fact that people were settled in a area from a date to the sort of industry those people were involved. Another possible way to confirm is through historical linguistics. A historian will examine the language that a culture speaks and compare it another cultures or a proto-language. Discrepancies in words can mean that a culture domesticated an animal or started using a certain resource at certain times. Along side the Oral history this can be used to create a fuller image of the past.

There will always be issues such as those mentioned by you, but those are generally things that the historians have trained for, for most of their careers. Where possible historians will work as closely as possible with translates to avoid bias and misrepresentation issues. The politics and personal motives behind sources is common place among the majority of sources a historian will come across. A lot of constructing history through oral histories is using the sources that one has as effectively as possible and getting the most possible from said sources.

In the same way that the other commenters have said, oral histories are generally measured for accuracy by weighing what's been told against what's likely and what other oral histories, written evidence, archeological evidence, and other sources have to offer.

Frequently, however, given that there's many ways in which oral histories can become factually fallible, it's often more useful to use them in a way that investigates meaning, rather than just mining for facts.

There's a great many oral histories that contain information that we either definitively know to contain factual inaccuracies or can reasonably assume to be factually inaccurate. That doesn't make them useless. Quite the opposite. The way we shape stories, remember things, and present our own histories can be a much more meaningful source of information about a person, culture, or event than just a basic recalled fact.

Sometimes oral histories are just as useful because they're not trustworthy - they're another piece of the big picture, especially when examining people and social histories.

You try to find differing opinions, or any other pieces of research that tell more of the story, so you can draw conclusions with as much information as possible. And if the only voice you can find is that of the powerful - you always keep that in mind in your research/analysis, rather than just going with what's available.

Historical work that relies on oral histories - and doesn't present them as such (i.e. sticks it in the footnotes with the rest of the sources, like any other evidence) is often very skewed, as you can imagine.

One good example/story of what not to do with oral histories, is the the comparison between history professor Victoria Bynum's book about a (complicatedly) mixed-race family/community in the antebellum South, The Free State of Jones, and the mainstream book on the same subject that came out after it.

Bynum used a lot of primary sources from the family and their descendents, but discussed the limitations, and talked about using them in context of one another to get a better understanding about the people and their perspective. It's even-handed and works to not romanticize the subjects or their actions. (I'm not saying it's necessarily perfect, but she does what she should with the sources.)

So, a couple years later, a book about the exact same thing came out, backed by a major publisher, called The State of Jones. There are many reasons it's not very good history (they clearly began with the intention to make the main character into a hero rebelling from within the South, when none of the evidence pointed to that).

But one of the biggest problems was that the authors relied on oral histories of family descendents as fact to fill in their narrative (again, without saying they were doing so), while those particular sources were known to be dubious and often totally incorrect. So because their base comes from skewed and biased information, the rest of it falls apart.

TL/DR: Don't use oral histories as if they're the same as factual accounts of the past. They represent how someone perceived or remembers something, which is extremely useful as long as you analyze it against other evidence.

(Or super useful if you are studying the social effects of something, and want the perception as opposed to the fact.)