They should not seem so bizarre-- they are simply square or rectangular wooden dishes/bowls with a thick finish (several coatings of lacquer). For osechiryori, which is composed of many different dishes, they are designed to stack. Real lacquer bowls are now quite expensive, and most people make do with plastic imitations (probably made in China).
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Mister MicawberYou'll get them in more traditional restaurants every day-- but they'll be the plastic ones.Thanks, Mister.