How can I make oatmeal cookies softer/more chewy?
More crunchy without eggs to moisten. 

Another factor is how long the mixture sits to absorb the liquid egg before baking. Longer = chewier

I use molasses and white sugar in place of the brown sugar and that also makes them more tender less crunchy.

Also adding 1/2c more oats to recipe will be chewier if they aren't over Baked/dry.