and arise, arise From death, you numberless infinities Of souls, and to your scattered bodies go, (lines 2-4)
The speaker sets up the "death-as-sleep" metaphor that will appear later. This is the big wake-up call, which means there will be a whole lot of groggy dead people.
All whom the flood did, and fire shall o'erthrow, (line 5)
"O'erthrow" probably means "bring about the death of" in this line. The Biblical "flood" killed everyone on earth except for Noah and his family, and the "fire" refers to the flames of the Apocalypse.
All whom war, dearth, age, agues, tyrannies, Despair, law, chance, hath slain, (lines 6-7)
The speaker lists all of the non-end-of-the-world-related deaths. These are all the ways that normal people can die. "Dearth" is starvation and "agues" means sickness.
But let them sleep, Lord (line 9)
According to this poem, death is just the "sleep" between the end of earthly life and the beginning of eternal life. It's funny how the speaker sounds like a nervous parent huddled over a crib: "They look so peaceful – let's let them sleep, huh?"
with thy blood. (line 14)
Jesus and God share the same bloodline as son and father of the Holy Trinity. God the Father wrote the pardon for humanity and sealed it with His son's blood.