I agree with Vincent, the most efficient way to learn the measure words is to be familiar with them by using them frequently. I say that because the original meaning of those measure words has evolved thousands of years, and even the native speaker do not understand their initial meaning unless they have to read ancient Chinese. The initial meaning of 件 is to separate things. After separation, you can distinguish one thing from another. Thus, 这件衣服 are different from 那件衣服. And documents can be separated by the papers that is written. Therefore, 这件公文 is different from 那件公文. Each 公文 carries different purpose when people write them. As a result, 件 is used to measure the purpose or intention, 这件事 is different from 那件事, from concrete document to abstract event/intention. Similarly, 把 is to hold things by your hand, as you can see the hand(手) at the left hand side of the character with 巴/ba1/ at the right hand side. So 把 is to count things that can be and should be hold with your hand：一把伞 一把铅笔 一把刀. 支 is to describe things that is thin and long like a stick. 一支笔，一支蜡烛，一支箭。

All of them are measure words which can be paired with different classifications of nouns. For example, in English, you can say 1 glass of water, 1 cup of water or 1 bottle of water. Glass, cup and bottle are just like words that you mentioned here. I advise you not to figure out exact differences between them. All you need to do is just to remember those typical expressions with them when you come across during your study. There are just a few. And gradually you will know how to use them like a native. I will give you some typical examples below. '件'： 一件衣服（one suit），一件礼物（one gift），一件商品（a commodity） '把'： 一把雨伞（one umbrella），一把手枪（one pistol），一把铅笔（several pencils） '支'： 一支铅笔（one pencil）， 一支部队（one group of army），一支乐曲（one piece of music） Hope this will help! Enjoy your Chinese learning!

一件毛衣，一件大衣，一件上衣，一件衬衫，一件东西，等等，都很大， 一把铁锹，一把锄头，一把筷子，一把铅笔（好几只铅笔），一把钢笔（好几只钢笔），等等，大且长的东西， 一支铅笔，一支钢笔，一支部队，一支队伍，一支人马，等等，细且长的东西