Wearing them in the rain might be all that is needed, though I remember my Navy greatcoat smelt like an old dog when it got wet. I wonder where that went -

However, if you do decide to was them you might find that human hair shampoo with conditioner is just as effective as any of the specialist washes - Woolite in particular is actually quite harsh on the fibres.

Rather than trying to rinse them after washing, use a shower, just lay them under the spray - if you have something you can lay them over so the water runs through them it will speed the process. I have a triangular airer which I lay wool over for rinsing after dyeing.

You need to have all the water at about the same temperature, and no rubbing or agitation so as to prevent felting - you might get some shrinking, but if you are careful if should be minimal.

Once the detergent is rinsed out a further bath in water with some white vinegar will restore the proper pH of the fibre. About half a cup is enough for a heavy jersey, so you'll have to extrapolate up to coats. One reason why wool garments are preserved in peat bogs is the acidity. You don't rinse out the vinegar water, just let it drain and dry off.