“平时”口语里见到的比较多(is oral language)。 “平常”还有另外一个意思，我是一个平常人。(another meaning can express that I am a ordinary woman. 有平凡的意思) “通常”比较书面。(in writing) “经常和常常”，经常比较常用。在意思上都没差别。

经常，常 and 常常 mean "often". Chinese words are sometimes doubled to emphasize the meaning, like 谢(to give thanks) doubled to 谢谢 means "thank you". 一点点 compared to 一点 means "an extreme small amount" . 你要不要加牛奶？-do you want to add milk? 我只想一点点- I just want a little bit. you can think of 常常 as "[very] often" 常常 compared to 常 emphasizes how frequent an action takes place. 我常常和我朋友去图书馆- I often go to the library with my friend. (this is almost like a daily routine) 平时 means "normally" and 平常 means "usually". As for 通常, according to my Chinese friend, it means "generally." Many of these are not that different from each other, just small but subtle differences.

平时只是一个时间状语，不具有重复概率的含义，意思与平常几乎一样。但是，平常还有另一个意思：普通的。比如：我是一个平常人，不是超人。 经常和常常可以互换，是表达动作重复频率很高的意思。比如：我经常不吃早餐，常常把早餐和午餐一起吃。不过常常更通俗，有时也单用一个常字。 通常表示在一般的情况下、不出意外的话，也有普通平常的意思；但是人们口语中不常使用，因为它有一定的文学意味（in written words）。比如：爱情通常会经历三个阶段。

平时 usually 平常 normal or ordinary. But it could substitute 平时 in some slangs. 通常 more often than not

我补充一点：平常可以是副词adv也可以是形容词adj，而平时、通常就只是副词adv。比如，平常人=ordinary man，平常心= normal mentality/attitude/mood, it means "take it easy and treat sth as usual"