I do not recommend touching the hilt unless you are very handy at woodworking. And even then, what I'd recommend is to just fill in the gap between the face and the nose with wood filler. Given the close proximity to the face, I thought you may have to carefully break the nose to do a clean job.
Sheath-wise, the gunk can be cleaned with a very diluted dishwashing liquid and steelwool. Be careful not to overclean it and take off too much of the old finish.
Blade is already pretty corroded. Maybe a stop-rust strategy might be better than to really clean off the rust?
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