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Tesselation is my new word of the day :-)
First thing I thought was high shelf on the back wall, with hooks (alternating front wheels and rear wheels), that's at least 4 bikes (maybe 2 with the washing machine), then using the left side side was to store at least 2 bikes horizontally, and maybe one of two more on the right using pedal hooks. Ikea Ivar is a good base to hack for vertical bike storage.
Please tell me you're planning to sort that room out and its current state is temporary...