One nickname I missed in the Terran section was an alternative one for the SCV, which is 人族最强近战单位 . This means "Terran's strongest melee unit".
You may see the character 虫 quite often, it means bug. Therefore the Zerg as a whole are named 虫族, meaning literally "bug tribe". Terrans are 人族, meaning human tribe (obviously), while the Protoss are 神族, or god tribe.
Ok so let's look at the names of the Zerg.
Creep - 军毯: Military carpet
Drone - 农民: Farmer. This name is the same for harvesters of all races.
Zergling - 小狗: Small dog. The official translation is 跳虫 which actually means jumping bug, but somehow everyone prefers to call them dogs.
Baneling - 爆虫: Explosive bug, 毒爆: Poison explosive, 炸弹虫: Bomb bug, 灯泡: Lightbulb.
Roach - 蟑螂: Cockroach
Note: 七仙女/八仙过海: Seven fairy girls/Eight immortals crossing the sea. Used to refer respectively to the early game seven roach rush and eight roach rush. http://en.wikipedia.org/wiki/Eight_Immortals
Overlord - 王虫: King bug, 房子: House (because he gives supply), 气球: Balloon.
Note: The supply depot and pylon are also referred to as 房子 (house).
Overseer - 眼虫: Eye bug
Queen - 皇后/女王: Both mean queen.
Note: 皇后 usually refers to a queen who becomes queen due to marrying into the royal family, e.g. what Kate Middleton will become some day. 女王 usually refers to a queen who becomes queen due to birthright or conquest, e.g. Queen Elizabeth II or Danaerys Targaryen. (it can also refer to a SM queen)
Hydralisk - 刺蛇: Spiky snake, 口水: Saliva, 吉祥物: Mascot. (see Terran section for explanation)
Note: In HOTS the Hydra has managed to shake off the Mascot title since it received the speed boost!
Infestor - 感染虫: Infestor bug
Mutalisk - 飞龙: Flying dragon
Corruptor - 鱿鱼: Squid
Nydus worm - 坑道虫: Ditch bug, 菊花虫: Asshole worm.
Note: 菊花(asshole) is sometimes used in Chinese to describe an overpowered unit (I think), however here I am not sure whether it refers to the Nydus worm's OPness or its shape...
Ultralisk - 雷兽: Thunder beast, 大牛: Cow, 大象: Elephant.
Broodlord - 大龙: Big dragon. This name was used for the Guardian in SC1.
Swarmhost - 宿主: Host, 西兰花: Broccoli, 莲蓬乳: Bubble breast. (ok well I didn't cook this up)
Viper - 飞蛇: Flying snake, 龙虾: Lobster.
That's it for the Zerg, I'll do Protoss tomorrow. Ah let me explain how Chinese players and commentators refer to buildings. Basically they do so via hotkey, according to race. So if the subject in question is a Terran, BB would refer to the Barracks, while VF would be the Factory. This is slightly confusing the first time one hears it.