According to your description, you mentioned that "I have problem with .docx,.xlsx files and that too after deployment only, mean in local machine it is working fine." Is that mean the .docx and .xlsx files can be downloaded success in storage emulator (local
SQL Server databse), but now works in Cloud Storage? or works fine at local machine with cloud Storage but not in cloud environment with cloud storage? And i suggest you provide more details about your exception message, such as Stack message or tracing logs.
And please following Steve's suggestion check "blob.Properties.Length-1" in HttpRequest Header.
Here is the difference between Azure Cloud Storage and Azure Storage Emulator: