촉촉하다 - You may feel very positively, with just enough moisture, get moist, moderately.
축축하다 - Soggy, soaked with water or any kind of liquid, but not very good feeling.
젖다 - Soggy, to get wet or soaked.
이슬에 촉촉히 젖었다. I get moist with dew.
옷이 축축했다. My clothes felt wet.
물에 젖었다. I got soaked.