All three poems are elegies, which are poems that mourn the loss of a place, person, item, or even state of being. Elegies are sorrowful in tone as a result. Though all three of these poems do not deal with similar losses, they do feature speakers who feel banished in one way or another, both literally and spiritually.
"The Seafarer" describes a retired sailor who misses his life on the ocean. Even though he is comfortable and surrounded by kinsmen on land, he misses the adventure of the often-hard life on the sea. It doesn't matter that he was uncomfortable or in peril on the sea; it made him feel alive. He feels like an alien on land, hence the sense of banishment. All of the speakers in these poems have lost the communal warmth of their former lives in some way.
"The Wanderer" is about a person who has lost his tribe. He remembers the mead hall where the warriors and their lord gathered to commune with one another. Though he was not literally banished from his people, he has lost them to death and thus considers his loneliness a kind of exile.
"The Wife's Lament" features a woman whose lord has left for a faraway land, and her attempts to follow him end with her forced to live in a hole by her husband's kinsmen. She lives in literal exile, unlike the other two poems, and her longing for her husband amplifies her sorrow.
The first two of the poems evoke heaven and the afterlife as the solution to these feelings of banishment. In heaven, there is communal joy and reunion compared to the ephemeral nature of life on Earth where people die. Interestingly, in "The Wife's Lament," the speaker seems too consumed with sorrow to find any transcendence in her banishment.