If you're in North America, most pilots use non standard phraseology. So learning by what you hear on the radio isn't exactly the best way to learn proper radio work. Instead, talk to flight crew who have flown around the world, from Europe to Asia, where english is most definitely not a first language and language barriers are clearly present. In such a context, saying things like " request 20 left" or "xyz is diverting left" will often get ATC confused.
If enroute, the proper phraseology is: "request 20 miles left/right of track due weather".
If in the terminal area under radar: "request heading 170 due weather" (note that you state the actual heading you need, instead of how many degrees of turn you want).
There's no need to explain the whole situation by saying there's a "CB ahead", or "we need to deviate around buildups", etc. Saying "due weather" is the enough and will always be understood anywhere you are. And that's the point with standard phraseology: it has to be easily understood by anyone, from the American in Chicago to the Taiwanese in Taipei. North American phraseology only works well in North America.