If it's needed right away, do very thin layers of chips, skimmed off the surface of the pile (as those will dry out the fastest) and build up layers over time. Like maybe a thin layer every 2-4 weeks or so. So it won't instantly fix your issues, but you should start to see some improvement...
Once deep litter gets going it'll eat up odor as it composts down the poop. Also rain is fine with it- provided that the soil in that location has good drainage and that you use a mix of components in terms of size, shape and material (chunky aged wood chips being an ideal base material for...