So, here we go. Add suka to every statement to sound more Russian. Or write using CAPSLOCK.

"Mid", "top", and "bot" stay the same.
GG stays the same.
Missing lane - ss or cc (cyrillic version)
Any action (kill, roshan, defense, offense) - just add go. E.g. "go rosha", "go b", "go def".
Roshan - Rosha (yes, without the "n")
Negative emotion - Mamku ebal, suka, v rot ebal
Positive emotion - molodec, zbs, zaebis
Laughter - lol, ahaha (notice that it starts with an "a")
If you got ganked because someone didn`t give a "miss" - gde ss suka (optional - GDE SS SUKA)
"Let's play defensively" - igraem ot defa
"Let's play offensively" - go go go, push, pronosim (mid, top, bot)
If someone did not connect to the game - Suka, opiat s kalkulatorov igraut ot just Kalkulator("Calculator", you get the joke)
Rune - runa
Leave the rune to me - ostav runu suka
Gank - kill (never say "gank")
Wards - vardi (e.g. kupite vardi suki)
Courier - kura (e.g. kupite kuru or gde kura bleat)
Buy something - kupite
A bad player - rak, dno, dniwe, or, in some cases, (\/)0_0(\/)
A good player - batya, otez
Won (a tower, the game, anything) - zatachil
Lost - proebal
American - Pindos
Russian - Russkiy (e.g. ya russkiy)
I - ya
You - ty (just like "thank you", e.g. ya batya, ty rak)
Thank you - sps
F%ck you - poshel na hui
Back - b (e.g. "ya b")
You snached the aegis! - SUKA SPIZDIL AEGIS
If someone is controlling the courier - SUKA OTDAI KURU or NE TROZH KURU
If you are going into the jungle -ya v les
Suck my magic stick - sosi suka, sasai
Overpowered - imba
You insulted me, and i seek for revenge - pvp ili zassal?
I am going to leave the game - Ya livayu
You are raging, and it is fun! - BOMBANULO or PRIPEKLO

Shaker - Borodach
Kunnka - Pistoletov
Treant Protector - Derevo
Io - Sosi debil ne budu sapportit`
Axe - Krasniy
Doom Bringer - Sotona
Chaos Knight - Kon` - Ogon`
Lifestealer - Gulya
Night Stalker - Balanar
Pudge - Tolstyak or Myaso
Ursa - 1 lvl Rosha
Slardar - Selyodka
Troll Warlord - Trall Warlord
Sniper - Stiler
Juggernaut - Yura
Lone Druid - Mishka
Riki - Krisa or odnoknopochniy` pidor
Bounty Hunter - Krisa
Drow Ranger - Drovka
Faceless Void - Zolotye Kupola
Templar Assasin - ONA TUT!!! (ping fiercely)
Venomancer - Venik
Rubick - Dendi
Chen - Chechen
Nature`s Prophet - Fura
Invoker - Pianist
Batrider - Batruha
Dazzle - Detsl
Ancient Apparation - Apparat
Silencer - Salo
Spirit Breaker - Kadilo
Broodmother - Mamka