A. which is also credited with having popularized the modern image of Santa Claus and having pioneered the use of product placement -- "credited with having X and having Y". Parallelism is intact. Relative pronoun "which" refers back to Coca cola and not "soft drink company"
B. which, while popularizing the modern image of Santa Claus, pioneered the use of product placement -- "while" is used to denote two parallel actions. This is completely wrong here since the "pioneering" came after the "popularising of Santa clause image". Eliminate
C. which, after being credited with popularizing the modern image of Santa Claus, pioneered the use of product placement -- Eliminate. 1. Incorrect use of being. 2. We don't need to put "popularising" phrase into a non-restrictive modifier or non-essential modifier.
D. which is also credited with popularizing the modern image of Santa Claus, pioneering the use of product placement -- Eliminate. Broken parallelism. "which is credited with X, pioneering the use". "pioneering the use" is parallel to "credited with X". The structure here implies a causal relationship which isn't true.
E. popularizing the modern image of Santa Claus and pioneering the use of product placement -- "we need a relative pronoun here to refer back to "Coca-Cola". Right now, this is making a general statement about "soft drink company" which isn't the intended meaning.