Knives
1,360 kills (perp: Petar Brzica) (year: 1942)
Guns
7,000+ kills (perp: Vasily Blokhin) (year: 1940)
Strangulation
5,000 kills (perp: Souflikar) (year: unknown; happened over a span of 5 years)
931 kills (perp: Thug Behram) (year: 1790 - 1840) (type: serial killer, not mass murderer like the rest)
Any others?