What are the criteria for inviting conference papers (e.g. SODA) for special issue? This is mostly for some immigration related document that I am trying to write and want to reference an online link which mentions that only a select few papers are invited for special issue for SODA conference. Also would be good to know about the selection criteria and the panel which selects it.
You may want to refer to the editorials introducing recent special issues: 

SODA 2016: https://dl.acm.org/citation.cfm?id=3230647

SODA 2017: https://dl.acm.org/citation.cfm?id=3319426

They both start with essentially the same paragraph:


  We are delighted to present a Special Issue of ACM Transactions on Algorithms, containing full
  versions of seven papers that were presented at the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017) in Barcelona, Spain, on January 16–19, 2017. These papers, selected
  on the basis of their high rating by the conference program committee, have been thoroughly
  reviewed according to the journal’s highest standards.


(Emphasis mine.)

For something more detailed about the selection process, you probably want to follow Josh's suggestion from the comments: contact the PC chair directly, and ask for a brief explanation, ideally printed on official letterhead. My experience is that the process of selecting the special issue papers is not standardized, but usually involves identifying the papers that received the highest scores, and/or collecting suggestions from PC members, and then possibly having some voting procedure.