Vim, 1818, 17 bytes
lqqyljvPkvPll@qq@qqqyljvPkvPll@qq@q This uses the V interpreter because of backwards compatibility. Input comes in this format:
string1 string2 Explanation:
l " Move one character to the right qq " Start recording in register 'q' yl " Yank one letter j " Move down a row vP " Swap the yanked letter and the letter under the cursor k " Move back up a row vP " Swap the yanked letter and the letter under the cursor ll " Move two letters to the right. This will throw an error once we're done @q " Call macro 'q' recursively q " Stop recording. @q " Start the recursive loop