In literature, when we talk about the uncanny, we are often talking in terms of Freud's famous definition of the uncanny in his essay of that title. Freud claims that "the 'uncanny' is that class of the terrifying which leads back to something long known to us, once very familiar"(1–2). With this definition in mind, the very juxtaposition you identify between the mundane and the fantastical that often lends itself to humor or anticlimax in American Gods can also easily evoke the uncanny.
For example, many of the old gods appear in very mundane settings and have taken on common jobs: Anubis runs a funeral home and Czernobog became "a knocker" in the meat packing business (76). In the novel, common jobs and industries can lead us back to powerful mythological figures who, as Gaiman suggests, were once very familiar to the people who came to America from places where these myths originated. This process of rediscovering something once familiar is part of Freud's characterization of the uncanny.
Yet, as you mention, many of Shadow's interactions with the old gods seem funny or anticlimactic. Shadow's interactions with the new gods, on the other hand, still incorporate this same process of leading the reader back to something once familiar, but Gaiman imbues these interactions with more of the horror and terror that Freud connects to the uncanny. For example, when Shadow first encounters Media, he exclaims, "Lucille Ball talking to me from the TV is weirder by several orders of magnitude than anything that has happened to me so far" (174). This is an odd statement as an actress talking from a TV is an everyday occurrence.
Gaiman continues to emphasize the normalcy of this scene, as Shadow later remarks, "It was a strangely familiar speech" in regards to the offer Media makes him to join the new gods (176). This scene, though, strikes Shadow as more disturbing than any of his previous interactions with the old gods. I find the end of this scene, when Media begins to undress in the form of Lucy in order to try to keep Shadows attention, the most unsettling. Here, we again see the uncanny, but the "once known" information Gaiman leads us back to is far closer to our everyday lives. As Media offers to undress, we are reminded that all the forms of media we spend so much of our time consuming will do whatever it takes to hold our attention and that this is the ultimate goal of all these sources of entertainment: to keep us watching. Most of us know this at some level but suppress it so that we can enjoy watching our favorite programs. Gaiman leads us back to this insight and, in doing so, evokes a sense of uncanny horror. This feeling of uncanniness is most likely stronger in Shadow's interactions with the new gods, because media and technology exert a far more immediate power and influence over our lives than old myths.
You also asked about real-life examples and, while I hope you find the example of Media in American Gods applicable to real-life, Freud expounds on a number of other common uncanny fears. He describes the fear of being buried alive as "the most uncanny thing of all" and claims that the root of this fear comes from the way it reminds us of our time in the womb.
The uncanny appears in many places throughout American Gods, but it seems to have the strongest resonance during scenes involving the new gods, as these revelations are more familiar to contemporary readers and lead us back to unsettling insights about our common practices and entertainments.