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 and Zokugo-dict.

I'm not Japanese, but as far as I know 「むぎゅむぎゅ」depicts squeezing something softly probably more than once as Sawa pointed out. I think you can use it in relation to some texture that has elasticity. The context it is used in can be cute, but is not limited to it. For instance, you see 「むぎゅむぎゅ」used to describe how the dough of a bagel feels. However, it is probably most common to use it when talking about skin or fat. Humorously, you can find some videos of cats on YouTube with descriptions containing 「むぎゅむぎゅ」.

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 and Zokugo-dict.

I'm not Japanese, but as far as I know 「むぎゅむぎゅ」depicts grabbing something softly. 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 and Zokugo-dict.

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 and Zokugo-dict.