The Japanese soldiers in the painting are wearing blanket rolls. The blue sashes are blankets or shelter halves, and within them, various personal effects would be rolled for ease of carriage while on the march. The ends are tied up together at the hip and this serves as a light-weight alternative to a traditional knapsack or similar pack which was often discarded, either as being too small, or too cumbersome for regular carry. Any additional personal effects that couldn't be folded comfortably into the roll due to shape, or any food items would often be carried in a haversack (the white bag on the soldier near (what I believe is) a Russian naval jack in the foreground that is lunging toward the Russian who's grappling over a rifle with a Japanese infantryman.

If you also note, the officers are not wearing these blanket rolls, because their belongings were part of the baggage train usually and they had aids and the like to manage their things.

Further, there's a two-fold purpose for the direction of wear of these blanket rolls with the tied end at the right hip, and the fold in the roll being at the right shoulder. The manuals of arms in most armies of the late 19th century (and through the first part of the 20th century) indicated that the positions of Carry Arms, Trail Arms, and Sling Arms (that is, various ways of carrying a firearm on the march) all required putting the gun up against the right shoulder. If the blanket roll is laid over the right shoulder, tied at the left hip, it interferes with the proper enactment of the various orders to carry your rifle. Also, while not really a reason that was ever officially given, a blanket is pretty thick, especially when rolled up, and can offer some small protection across the torso. Worn left shoulder to right hip, the blanket can incidentally offer some protection for the heart, which is absent when worn right shoulder to left hip.

EDIT: A few technical adjustments.

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