This is just an additional note on your question. The meaning of Old English poems is not so much affected by alliteration as it is carried by alliteration. Alliteration is a common versification technique in Old English poetry. In fact, in Old English poetry, alliteration was a required (or expected) technique and was far more important than rhyme. And if we keep in mind that Old English poetry--like The Seafarer or Beowulf or The Battle of Maldon, for example--was an oral poetry meant to be spoken and remembered--we can see how alliteration could have helped an audience commit such poems to memory--the repetition of sound helps to establish memory patterns.
We can see alliteration, rather than rhyme, working in these lines from Beowulf
. . . Then came in the wan night,/the stalking shadow-walker./ The spearmen slept,/those who in the horn-gabled hall must guard . . . .(ll. 702-704)
I think you can see here that alliteration doesn't have an affect on meaning, but it does help convey experience in such a way that fosters the listener's ability to remember what he or she has heard. And, as I noted above, alliteration is a technique that Anglo-Saxon listeners both expected and appreciated.
The alliterative technique carried over to Middle English poetry and has been used by poets in every century
"The Seafarer" is an Anglo-Saxon poem which relates, in part, the woes of being a man of the sea. It was originally written as a poem which would have been sung or recited by traveling scops (storytellers) as entertainment after dinner.
Alliteration, of course, is the "repetition of an initial sound in two or more words of a phrase, line, or sentence. It is usually a consonant and marks the stressed syllables in a line of poetry or prose," according to the eNotes "Guide to Literary Terms," linked below. (Think about tongue-twisters, which are alliteration in high gear, as in "Sally sells sea shells by the seashore.")
In this poem, lines 59-62 do contain plenty of alliteration.
My soul roams with the sea, the whales’
Home, wandering to the widest corners
Of the world, returning ravenous with desire,
Flying solitary, screaming, exciting me.
Notice the "S" sounds in "soul" and "sea" (and the additional "S" sounds at the end of "roams" and "whales"). This is followed by the "W" sounds in "whales,'" "wandering," "widest," and "world." Then the "esses" return in "ravenous," "desire," "solitary," "screaming," and "exciting" (remember it is the sound of a letter rather than the letter itself).
So we have a bunch of words with the "S" sounds and the "W" sounds. Notice the shapes of the letters and compare them to the tossing, rolling waves of the sea. The alliteration serves to reinforce the movement of the ocean, the flight of the birds, and the surfacing of the whales.