As far I know:
signal strength is high if wavelength is high
wavelength is low if frequency is high
Nope, they are inversely proportional. Wavelength is short if frequency is high. (EDIT, if by low you mean 10 cm is lower than 20 cm, then you're correct. Saying it's a low wave length is confusing because you don't usually use low or high for distance but short and long. Low and high is usually reserved for describing time or height not length.)
So signal strength is low if frequency is high
Nope, see first nope.
Signal strength and frequency (or wavelength--they are the same thing really) have nothing to do with each other. Signal strength is due to the transmission effective radiated power, the pass loss to the receiver, then the receiver's antenna+system gain. Factoring into this is the bandwidth used, the modulation type and the channels noise floor (the commercial FM broadcast band has a higher noise floor than just the thermal noise floor due to the extreme power used in that band). However for the geeks out there: the receiver signal strength is usually a measure of the IF amplifier’s amount of saturation through multi-stage amplifiers and is envelop based. This is actually a relative amount and is meaningless by itself until it is calibrated against a known input power level, then the amount of saturation can be compared to a calibrated input power level and thus a "signal strength" in dB can be estimated.
Anyway, among other things path loss can vary over frequency, but the FM broadcast band does not experience path loss differences from the low end to the high end because the band is too small to experience propagation differences.
The FCC tends to try to separate high power signals (commercial) from low power public broadcast signals (College radio, etc.) by putting them away from each other in frequency. That is why you often see the college/public stations in the 89-91 Mhz range and the big nationally syndicated stations at higher frequencies.