Osmosis is the diffusion of water. Water will travel down a concentration gradient. This means that water will travel from where there is more water to an area where there is less water. (In other words, water will travel from an area of higher concentration of water to an area of where there is a lower concentration of water). Thus, the greater the concentration difference, the greater the influx of water. Out of the three solutions listed within the question, pure distilled water would have the greatest concentration difference from the potatoes (which is essentially concentrated starch with little water present).
For this reason, the potatoes strips that are placed in the distilled water will get "mushy" the quickest. The potato strips that are placed in the diluted salt water will become mushy second. The potato strips placed in the highly concentrated salt solution will take the most time to become mushy.