Passports (Symbol)
The passport symbolizes the arbitrariness of human-made systems. Here, it grants its owners the status of personhood within society at large. This means that the speaker's lack of a passport robs them of their personhood. Though they are still alive, without a passport they are legally, though arbitrarily and illogically, considered dead. Meanwhile, the speaker reflects ruefully, passports do not simply renew themselves: unlike trees, they aren't subject to the cycles of nature. In this sense, the passport also signifies the unnatural and arbitrary strictures that humans force one another to obey.
Poodle (Symbol)
At one point, the speaker encounters a poodle wearing a jacket. Since poodles don't generally dress themselves, we can assume that a doting human put the poodle in the jacket. The spoiled poodle is juxtaposed with the speaker, who is, in contrast, completely rejected by broader society. Auden isn't so much making a case against dog jackets as he is making the poodle into a symbol of dehumanization. If people are able to devote so much care to a dog while ignoring or actively avoiding a human, they must believe that the human is actually not a full or real human (in this sense, the poodle and the passport are similar, with the former symbolizing social dehumanization and the latter symbolizing the official withholding of full human status). The fact that the dog likely doesn't want or need a jacket only deepens the symbol's impact. Just as dog owners might be able to project an imaginary persona onto an animal, imagining it to have wants and needs that it doesn't actually have, people are able to project an imaginary persona onto a human, in this case imagining that this human lacks ordinary, universal needs and desires.
Tree (Symbol)
In contrast to the passport, which symbolizes human-made structures and systems, the yew tree in "Refugee Blues" symbolizes nature's more forgiving systems of growth and rebirth. Though the yew tree the speaker describes is "old," it "blossoms anew" every spring. This is despite the fact that it is located in a cemetery, a site of death, and this contrast only strengthens this symbolic role. The tree's yearly rebirth is, like naturally caused death, part of a healthy and normal cycle of life. This is in contrast to the death and stagnation caused by humans through war, genocide, and deprivation.