The tides from the two major moons in such a system would be interesting- the two smaller moons would probably have little effect, but the other two moons would each cause tides, which would periodically reinforce each other, and would also each be periodically reinforced by the central sun or suns.
Each time one of the two moons is aligned with the other, or with the two suns in the centre (which would act, most of the time, as if they were only one sun for tidal purposes) there would be a high tide. In the case where there is only one sun in the centre of the planet's orbit and another several AU distant, I suspect that the second sun would have little tidal effect.
Note that 'aligned with' means that the objects concerned form a line with the planet; they can both be on one side of the planet, or on opposite sides. An extra big tide would occur when the two moons were both aligned with the central sun or suns.
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