The poetry of the Anglo-Saxon period was overwhelmingly elegiac. What this means is that the poems told the story of a person's life by revealing the personal thoughts and feelings of a single speaker.
These poems were also considered lyrical in the fact that they denoted the thoughts and feelings of a single speaker and spoke about the events in the speaker's life.
Not only did the poems speak to the events within one's life, the poems also had lyrical elements. What this refers to is the fact that the poems of this period were typically sung. With no global, or even local, language, the epics and poems of this period were sung.
Therefore, all three poems, "The Wanderer," "The Seafarer," and "The Wife's Lament" were elegiac and lyrical. The fact that each poem revealed the thoughts and feelings of someone other than the storyteller, or scop (the singer who told the stories) would easily be able to take the feelings spoken of in the text and tell them filled with the same emotion.
Another way to examine this would be the fact that it did not happen to the scop. It is much easier to tell a story which is not yours. The emotions revealed in all three of the poems is, at times, gut-wrenching. It would take some distance from the poem to be able to tell it without breaking down.
At the same time, one last idea to examine, the wanderer and the seafarer are no longer "here." They have moved on. Both have found peace with where they are and in their faith. That being said, a scop would have no choice but to tell another's story.
Poetically, all three contain very distinct elements typical of the period. All three contain kennings (metaphorical phrases used to heighten the language--make it more beautiful), alliteration (the repetition of consonant sounds within a line of poetry--adds to the lyrical "voice" of the poem, and assonance (the repetition of a vowel sound within a line of poetry--offers same lyrical "voice" as alliteration).
Direct examples of these, from the poems, are:
"Paths of exile" (meaning the ocean) from "The Wanderer"- kenning example.
"Bark's bows" from "The Seafarer"- alliteration example (the repetition of "b" in both words.
"I make this song of myself, deeply sorrowing" from "The Wife's Lament"- assonance example (the "o" sound in "song" and "sorrow").