Bristleback interaction with abilities and effects that doesn't have explicit direction

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How does Bristleback (ability) of Bristleback (hero) interacts with such damage sources:

Cleave damage from attacks
Damage-over-time (Venomancer's poison string, Viper's Corrosive Armor, Jakiro's Liquid Fire etc)
Spells that doesn't have flying projectile (Luna's Lunar Beam is likely to strike from heaven not from Luna to target, Zeus's Thundergod's Wraith etc)

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Dota 2 Hero Spotlight - Rigwarl the Bristleback

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Images: Gustavo Fring, Ketut Subiyanto, Elina Fairytale, Andrea Piacquadio