What are nonstandard forms of written words called? Normal characters are (汉)字 and nonstandard characters are 俗子.

Wrongly written words or nonstandard forms of written words can be referred to by using 俗作.

For instance, the entry for 耳食 in《南充方言词语考释》says:


  “耳食”俗作“耳屎”、“耳视”等。


What are these types of words called? 

异形词 is an, obvious, option. I would like to be more specific noting that it is a 俗 problem.

俗词 would just talk about current terms or expressions, vulgarities or familiar language.

What is the proper term for nonstandard forms of written words?
异形词 is the broad term.

A more specific, albeit obscure and probably not widely accepted term would be: 俗体词.

Usage of 俗体词 can be found on this Zhihu question: 英译中里俗体词和异音词如何处理？ 


  俗体词（比如错音错意、用词不当等）


Although it is talking about English, it should be clear enough to be understood in Chinese as well.