This is just a summary of my initial notes. In some cases, it's possible to get a real count based on the text of each song; in others, one has to guess, estimate, or extrapolate. I've included any instances where it seems clear that (within the setting of the song) someone has actually died in the past or is about to be killed (imminently). I have omitted songs are about death in the abstract, death personified, or mortality as a condition. I have included songs that are fanciful but depict a death as such, but omitted songs (such as "Dirty Knife") in which a death, while vivid, seems to be illusory.

Canadian Amp

2 - Make Your Bed (One murdered by hobo, one about to be murdered by hobo)

2 - Ellen Smith (One murdered, one about to be executed for murder)

2 - In California (Anonymous suicide, Black Dahlia, both mentioned only in passing)

1 (animal) - Favorite (Deer hit by car)

Blacklisted

459 - Deep Red Bells (Interstate serial killings: At least one is indicated in the song, but it refers to many unspecified others. A quick bit of googling turns up famous highway killer counts in the 8-44 range, but if the song is speaking about highway serial killings as a general phenomenon, USA Today reports that the FBI gives 459 as a four-decade total.)

96 - Lady Pilot (Song refers to people trapped alive during the process of constructing a dam; based on surrounding lyrics, seems reasonable to assume it's the Hoover Dam. There are various numbers used for this, but 96 seems to refer to actual deaths during the construction process, which may be as close as a casual investigator can get to the specific number who might have been buried or crushed.)

Fox Confessor

1 - Star Witness (The song is a bit ambiguous, but it seems like probably at least one person is dead in it. Possibly more, but hard to say.) Update: Confirmation courtesy of zesticola.

1 (animal) - Maybe Sparrow (Titular sparrow, possibly killed by hawk?)

Middle Cyclone

161 - This Tornado Loves You (I went with 161, because that is the most recent (2011) tornado to make the list of 10 deadliest tornadoes on Wikipedia. My reasoning is that the narrator appears to be an unusually destructive tornado with a high cost in life, but that (unlike most of the very deadly tornadoes in US history) it appears to be occurring in more less the present day.)

1 - People Got a Lot of Nerve (Mauled by Orca)

1 - Polar Nettles (Death at hospital? Manner unclear.)

Tigers Have Spoken

1 (animal) - Tigers Have Spoken (Tiger euthanized.)

1 (animal) - Favorite

1 - Hex (Death by titular curse.)

Furnace Room Lullaby

1 - South Tacoma Way (Song addressed to a deceased person, reference to their funeral)

The Virginian

1 - The Virginian (Summarizes a character's life, death, and afterlife. Nature of death not specified.)

Update

zesticola: (re: Neko Case Album Mortality) Neko has said that Star Witness is about a person that was shot on the street where she lived (I think in Chicago, but maybe Seattle) and he bled to death there on the street. The paramedics took their sweet time getting there and didn't bother doing a lot to help because the victim was black (hence "they don't even put on the siren"), the song is narrated from the POV of a relative of the victim. So yeah, definitely a death there.

Nice, thanks!