It's fair to say that there are a number of ways one can interpret these sorts of accounts.

The first is to take them at face value and then try to find natural phenomena to explain what might be behind them.

The second is to take them at face value and find some extraordinary phenomena to explain them: having taken this approach, you can then make a 52 minute documentary of what you have concluded and it will be purchased by History Channel's Ancient Alien series.

The third choice is to accept the fact that people recount unusual phenomena, whether they existed in reality or not, and in the process of recounting them and having others carry the tales forward, the phenomena become more extraordinary in the telling.

We are constantly faced with unusual phenomena, and we interpret what we have encountered with the inventory of explanations at our disposal. A modern, scientifically-bent mind will seek natural explanations for unusual phenomena, but there are plenty in our midst who will see something strange and attribute it to the realm of the extraordinary if not the supernatural.

I was just editing a passage from a book I am developing, which fits here: "Strange and remarkable things exist in the world. Unusual events have always amazed people and beg for explanation. It is human to attempt to understand. As children of the Scientific Age, modern humanity smugly congratulates itself for not being superstitious, but less than might be expected separates the present from the past. Peculiar lights become aliens, even though technology fills the sky with all sorts of human-made hardware. Crop circles become proof of aliens, even though it may be easier to look at the bored farmer with just the right sense of humor to pull off such a prank. Seeking exotic explanations for the extraordinary is nothing new, and the sophisticated modern age has not extinguished the practice. In a pre-industrial setting, however, the inclination to see the actions of the supernatural was far greater."

You can handle your bizarre accounts in primary sources as you wish, but a folklorist will tell you that one need look no farther than in the soul of humanity to find an explanation. The unusual demands attention and its retelling yields elaboration. And where there is nothing at its core, the imagination of the folk creates the unusual and makes it even more remarkable. It is our nature. Which is, in fact, natural, and yet it presents a direct path to the supernatural.

Hello! Things like this come up quite regularly in ancient literature as well, and while it is tempting to dismiss them as fantasy or ignore them altogether, we must remember that supernatural phenomena seemed real enough to most people. Of course, we might then try to rationalize these phenomena with natural explanations, but ultimately I find it more meaningful to simply acknowledge that people believed them to be true.

This is basically how Ramsay MacMullen addresses the issue in Christianizing the Roman Empire, A.D. 100-400 (New Haven: Yale University Press, 1984). He notes that not believing in miracles would have appeared utterly "irrational" to the average ancient, that "people are capable of keeping nature and its law and ordinary life in one compartment of their minds and something quite different in another" ("Galen the true scientist, for example, who believed in centaurs and yet didn't"), and that "it gave pleasure both to relate to hear wonderful stories, because such is human nature..." On his own approach, Ramsay states: "...I report as faithfully as I can what people of that ancient time believed. On their beliefs they based their actions. Beliefs and actions together are realities. The historian who sticks to those sticks to his last." This seems pretty reasonable to me. :)

The first chapter of the book Fiery Shapes: Celestial Portents and Astrology in Ireland and Wales 700–1700, which focuses on the interpretation of astrological phenomena, may give you some ideas (though it does not tackle directly the problem, but rather tries to understand the making of the literary description of portents). Another possible lead (which I think was proposed to me in a tutorial a few years ago; it may ultimately come from Martin Heinzelmann) is that churchmen considered that it was important to record everything (even second or third-hand information) because “you never know,” and that each of these signs could become, in retrospect, an important eschatological key.

So an important thing to consider is that many of the things that we'd consider "weird" wouldn't appear so to a medieval thinker. Imagine you're a relatively learned medieval thinker and you hear a report about the sighting of a unicorn. Well, you think, unicorns appear in the Bible, they're mentioned in encyclopedias, in bestiaries, in travel narratives, and in the writings of the Church Fathers, essentially all the meaningful authorities that a learned man would draw on to shape his picture of the natural world. So why wouldn't you believe such an account? Sure, you've never seen a unicorn, but you've never seen Jerusalem either, and you're pretty darn sure that it exists.

Likewise an apparent miracle or wondrous event. Every reputable source assures you that these occur, and not only occur but occur regularly. Why on Earth would you doubt them? Yeah, you may not have ever seen a miracle yourself, but, then again, you've never seen a naval battle either.

I've tried looking for literature about weird stuff reported during the medieval period but couldn't find anything.

I'm not quite sure what you're asking for here, can you be more specific? As a lover of all things medieval and many things weird, I might be able to help.