We present a study of the multiwavelength (MW) variability of the blazar AO 0235+164 based on the radio-to-gamma-ray data covering a long time period from 1997 to 2023. The radio data are represented by the 1-22GHz measurements from the SAO RAS RATAN-600 radio telescope, the 5 and 8GHz data from the IAA RAS RT-32 telescopes, and the 37GHz data from the RT-22 telescope of CrAO RAS. The optical measurements in the R-band were collected with the SAO RAS 1-m Zeiss-1000 and 0.5-m AS-500/2 telescopes. Additionally, we used the archive data at 230GHz from the Submillimetre Array and the gamma-ray data in the 0.1-100GeV band from the Fermi-LAT point source 4FGL-DR2 catalogue. The variability properties during four epochs containing major flares and one epoch of relatively low activity were analysed using the fractional variability indices, discrete correlation functions, Lomb-Scargle periodograms, and structure functions. A significant correlation (>=2sigma) between the radio, optical, and gamma-ray bands is found for all these periods with time delays from 0 to 1.7yr. The relation between time delay and frequency is described by a linear law with a negative slope of -10d/GHz. The discovered properties of MW variability for the low-activity period and for flaring states suggest that the mechanisms dominating the radio-gamma-ray variations are not substantially different. The detected quasi-periodic oscillations of about 6 and 2yr are tentative, as the time span of the observations includes fewer than four full cycles for the radio and optical data and only about three cycles for the Fermi-LAT data. These results should be interpreted with caution, given the limited number of observed cycles and the influence of red noise. We used cluster analysis to reliably separate the high and low-activity states and determined statistical differences in the main properties of AO 0235+164 non- thermal emission. The physical parameters of the radio jet were obtained using the Hedgehog model applied to the average radio spectrum of AO 0235+164 in the range 0.1-300GHz. The effectiveness of replacing electrons with protons in the synchrotron radio emission of relativistic jets is shown for describing the nature of blazars and the generation of high-energy neutrinos.