Of course there was! The pre-Christian Norse people had a centuries-old verbal tradition, and skill in poetry was highly valued. We know this through recorded examples toward the end of the “Viking” age, such as the Icelandic sagas and the poetic and prose Eddas. At least some, of not most of the literary evidence we have was recorded in the 13th c. by a royal Icelandic poet named Snorri Sturluson, who wrote down as much of the old poems and stories as possible in an effort to preserve this dying tradition, in a post-conversion Iceland where practicing the pagan faith was a crime and reciting old poems about the gods was frowned upon. During the middle years of the “Viking” era, it was expected of wealthy and influential men to be capable of composing and reciting some poetry. Professional poets might travel between households and courts- these people were known as skalds. As the mythology of the Norse people was so closely linked to the poetic tradition, these skalds were highly valued and revered. Not all poetry was so solemn, of course. In the sagas- moral parables and stories about such famous “heroes” as Egill Skallagrimson and Njal Thorgeirson- we read of poetic insults exchanged between rivals, short poems composed on the site of a great battle, and even mournful elegies composed by bereaved brothers and fathers. The best thing about the sagas, IMO, is the extensive mentions of the lineage of each character. One’s lineage was of great importance in medieval Scandinavia and Iceland, and continues to be to this day. Strict records were kept through recitation and eventually written down, so we can trace these famous lineages many centuries back to prove that the characters in these sagas really existed. Archaeological evidence and carved runestones often can prove that the events described really happened, too. The general form of a skaldic poem is four beats per line, with heavy use of alliteration. Rhyming between lines was not used as much as repetition of key syllables within a line or a couplet. This format was in wide use by at least Snorri’s time.

Yes., there is a large body of poetry and song inspired by the actions of famous Vikings.

There were two main types of poetry, skaldic and eddaic, the latter being the older more "classical" style of e.g., the Poetic Edda and skaldic being the more modern "court poetry" with many embellishings (i.e., so many kennings you begin to drown in them).

In this great article, it notes one of the many famous Norse poets: Egill Skallagrímsson, author of, among other works, Head-Ransom and Loss of a Son (see pg 88 of this for an article on the former). Another famous example is Bragi, who wrote the Ragnarsdrápa, which was composed for a Scandinavian king in honor of the hero Ragnar Lodbrok. (You can look at more skalds here.)

Snorri Sturluson's Prose Edda is in fact effectively a manual on how to write skaldic poetry, especially its section Skáldskaparmál, a list of kennings situated in a dialogue between Norse gods. (It should be noted the time period we're talking here is around 800 to 1200 A.D., in which time we know of over 300 skalds.)

Skaldic poetry was called court poetry for a reason - it was often commissioned for members of the court and performed at court. This poetry, though, also served another purpose - it was an oral history, meant to be passed down by bards at taverns and mothers telling tales to their kids, much like Homer was to the Greeks.

I personally find that norse poetry has a beautiful rhythm to it - the poetic form focuses heavily on alliteration, with a set number of beats per line (which varies depending on the type of poetry), with important syllables repeated for emphasis.