Q: Use of 'still' in present continuous tense 
John is still reading the book.

The above sentence looks odd to me. The use of 'still' in present continuous tense is not correct I guess? Right?

A: It is perfectly fine to use still in a present progressive sentence:

(10 a.m.) Mom: What's John doing? We have to leave soon.
Dad: John's reading a book. I'll tell him to get dressed.
  (11 a.m.) Mom: We have to leave in 15 minutes. Is John ready yet?
Dad: Nope. John's still not dressed and he's still reading his book.  

Here's a typical scenario. The fourth sentence uses still appropriately with the simple present and with the present progressive.

A: As shown in an example sentence on the OALD, it is fine to use still with the progressive tense.

I wrote to them last month and I'm still waiting for a reply.

The definition given for still from that dictionary is "continuing until a particular point in time and not finishing."
The difference between "John is still reading the book." and "John is reading the book." is that the first says that John was reading the book before, and he is now reading the book; the latter doesn't say anything about what John was doing before reading the book.
"John is still reading the book." could be used, for example, when somebody checked what John was doing and checked it again later; if that person noticed that both the times John was reading the book, that person can say that John is still reading the book.
