Tinker is voiced by Harry S. Robins, who has done numerous voices for Valve's hit First-Person Shooter series, Half-Life. Many of his lines make reference to, if not direct quotations from, the series.
Lich has a particularly specific line when casting Sacrifice:
Axe's ultimate, Culling Blade, is colloquially referred to as a "Dunk" due to the jumping motion he makes prior to bringing the weapon down overhead on the target, much like a basketball dunk. It's also referred to as Culling Beard, as part of his manly nature.
Bloodseeker: "Pubseeker", due to his high popularity in public / pickup games. He also goes by the moniker "Bloodcyka" for his popularity among Russians in the low-skill brackets note the curse word "сука" is synonymous with foul-mouthed or uncooperative Russians in the fan community.
He's also sometimes referred to as "Race Car" and "Ferrari Seeker" due to the 6.79 patch which completely removes his speed cap when his Thirst passive is triggered.
Dark Seer: "Sonic" or "Sanic" due to the spikes on his back giving him the appearance of a hedgehog, and his Surge ability allowing him to GO FAST.
Disruptor: "Dis Raptor," given his mount of choice.
The Hellbear neutral camp is referred to as "Tomato and Potato," due to their colors (yellow and red). It even ties in with the term "farming."
Huskar is occasionally referred to as "Michael Jordan" since he jumps at the target with an overhead stabbing motion when casting Life Break, similar to Axe's ultimate.
Lion's Aghanim's Scepter version of Finger Of Death which has an AoE, shown as multiple beams, is referred to as Fist of Death.
Nature's Prophet: His original name in DotA was Furion, but this was changed in the transition to DotA 2 due to copyright reasons. However, his actual name (prior to it being redacted) is very rarely used due to being unpopular and Furion is frequently used instead. The game files still refer to him as Furion.
Keeper of the Light shares this name, as his Aghanim's Scepter gives him the same effect in daytime as Night Stalker's does at night.
Phantom Lancer: "Cancer Lancer" or "Phantom Cancer" due to his rapid multiplication and the ability to win even the most hopeless games by "infesting" all the lanes with powerful illusions.
Related: Gyrocopter was "Chemocopter" during Phantom Lancer's heyday, due to Flak Cannon damaging the entire "Cancer Lancer" army at once.
The item Rod of Atos is sometimes called the "Rod of Aui," after competitive player Aui_2000, one of the few pro players who advocates its utility.
Slark: "Fishi", due to his appearance and (as a ganker) inevitable comparison to Riki.
Spirit Breaker: Space Cow, after the PyrionFlax guide to Spirit Breaker. This later became an Ascended Meme with the Three Spirits patch; Earth Spirit refers to him as a "space cow" in some of his responses. Another name that's gaining some traction is Spirit Baker.
Venomancer: "Bananamancer", due to his old model's curved posture and bright yellow-green color.
Warlock's ultimate Chaotic Offering is sometimes referred to as the "Dropping the Rock" as a nod to its original name in War3 Dota, Rain of Chaos, in which the Infernal would fall from the sky. It was changed to its current form since both Rain of Chaos and the Infernal are owned by Blizzard.
Windranger: "Windginger", because she's a redhead. note and because fans didn't like her name being changed from Windrunner
Witch Doctor: "The Walking Fountain," because of his constant AoE heal and ultimate. His ultimate is given the name "Dubstep Ward" for its sound effect. "Magic Coconut" is a semi-common name for his Paralyzing Cask spell, especially when it achieves some truly impressive bounces.
Zeus: "Mario," since his model design (one of the earliest and worst in the game, to the point where Valve have restricted additions of cosmetics to him until the model is redesigned) bears uncanny similarities to Nintendo's mascot.
Chris C, a developer at Valve, is frequently nicknamed "Bot Guy", as he's often the only one who works on the AI hero bots.
Hey, It's That Voice!: A lot of the voice actors worked on Valve's previous games, so it's not surprising to hear familiar voices.
Screwed by the Lawyers: Many Heroes have had their names changed from their initial iterations since they bear similarities to characters from Blizzard franchises (the main issue coming from the Blizzard-Activision merger making lawsuits a very real possibility):
Brewmaster was previously Pandaren Brewmaster. Due to the Pandarens being a World of Warcraft race, the "Pandaren" was removed and his design was shifted to resemble the red panda.
Similar to the above, the three Spirits (Storm, Ember and Earth) used the Pandaren model in the original War3 Dota, and had their designs changed to more closely resemble humans. In the case of Earth Spirit, who was created long after Dota 2 became its own game, his Dota 1 model was still a Pandaren for the sake of consistency.
Magnus is referred to as Magnataur in the game files. The Magnataur are a race in the World of Warcraft universe, so the Magnoceros race was created in its place.
Nature's Prophet had the name "Furion" in Dota 1, being a shortened version of "Malfurion Stormrage," a prominent WarCraft character.
Necrophos was originally known as Necrolyte (and is still referred to as such in the game files).
Outworld Devourer's original name was Obsidian Destroyer, based on a Warcraft III unit, so his initial Dota 2 name was Outworld Destroyer. It was very briefly changed to Outworld Demolisher, and then again changed to the current Outworld Devourer. Some fans jokingly refer to him as Ongoing Developer due to this.
Windranger was originally known as Windrunner. The change came due to Windrunner being the surname of a prominent family of heroes in the WarCraft universe.
Wraith King was originally Skeleton King, who was based on the Diablo character King Leoric. The entire Frostivus 2013 event was created around the complete change in his appearance.
Talking to Himself: Despite having well over a hundred different heroes, there are scarcely more than ten or twenty voice actors to give them all voices. While some of these are fairly obvious (Anti-Mage, Beastmaster, Necrophos and Warlock are all voiced by Sam A. Mowry, and sound like the same person at different ages), quite a few are very surprising (Crystal Maiden, Drow Ranger, Enchantress, Mirana, Phantom Assassin, Spectre, and Vengeful Spirit are all voiced by Gin Hammond, and Timbersaw, Bristleback, Skywrath Mage, and Abaddon are all voiced by TJ Ramini).
This can reach its peak when certain Heroes give responses after killing others.
Trope Pantheons: Several heroes has attained their places in the Trope Pantheons. While Zeus technically also made it in, he's more based on his God of War incarnation. Same goes to Medusa, being more based on the original mythological creature. True to the rivalry with League of Legends, all of these heroes list the League champions as their rivals.