MIT Public Class 6002: Electrical Circuit & Electronics

You actually have very good writing skills for a student your age, especially considering that you are an engineering 'nerd' :) -- not even an English major. Your vocabulary is good, and the sentence structures are very good. You just need to hone in on common syntax and idioms, which can only come with reading and practice. I have picked a few items below that I believe will help you improve your writing skills.  "your writing"  ... and ... "my corrections"

"... have seen a heating PBS drama 'The Big Bang Theory'."

"... have seen the popular American TV sitcom 'the Big Bang Theory'."

[ I really don't know what meaning you were intending, but the word 'heating' is wrong for this context. I replaced it with 'popular American'.  PBS stands for Public Broadcasting System, which doesn't carry this type of show. It is actually on CBS and TBS in America. Also, it is a 'situation comedy' – short form, 'sitcom'.  A 'drama' is a show with serious story line.]

"The cute Indian nerd Rajesh who always speaks with a strong accent is very popular among Chinese students in the show."

"In the show, the cute Indian nerd Rajesh, who always speaks with a strong accent, is very popular among Chinese students."

[ Your construction sounds like Chinese students are in the show. Also, commas are needed to isolate the dependent clause describing Rajesh. ]

"However, when there is no subtitle, I found it quite hard to understand any single word with an Indian accent."

"However, when there are no subtitles, I find it hard to understand a single word of his Indian accent."

[ "I find it hard to understand ..." is less formal syntax. "I find it quite difficult ..." is more formal. ]

"Recently, I am working on ..."

"Recently, I have been working on ... "

[ "I am" is present tense, as in, "Now, I am working on ...".  The recent past action that is still continuing requires the Present perfect continuous. ]

"The strong accent just drived me crazy!"

"The strong accent just drives me crazy!"

"Today, I watched one of his original class which has no tranlation; It is about ..."

"Today, I watched one of his original classes which has no translation.  It is about ..."

[  "One of ..."  is selecting from a group, i.e. more than one, which needs a plural noun – 'classes' ... as in, "one of these boys", or, "one of the best movies".  I also notice that you used a semicolon ( ; ) twice in this writing, with both constructions being grammatically incorrect.  The semicolon is rarely used outside of very formal writing these days, and I recommend you simply use a period and start a new sentence. ]