I'm not Japanese, but as far as I know 「むぎゅむぎゅ」depicts grabbing something softly. I think you can use it in relation to some texture that has elasticity. I'm not sure why, but I wasn't able to find it in a dictionary to my surprise.

However, I know of two dictionaries that might be able to help which have entries for onomatopoeia or 擬音語. 

Those are [Nihon Jiten][1] and [Zokugo-dict][2].


  [1]: http://www.nihonjiten.com/nihongo/giongo/index.html
  [2]: http://zokugo-dict.com/