Drifting pulsation structures (DPSs) are considered to be radio signatures of the plasmoids formed during magnetic reconnection in the impulsive phase of solar flares. In the present paper we analyze oscillations and waves in seven examples of drifting pulsation structures, observed by the 800-2000 MHz Ondrejov radiospectrograph. For their analysis we use a new type of oscillation maps which give us a much more information about processes in DPSs than that in previous analyzes. Based on these oscillation maps, made from radio spectra by the wavelet technique, we recognized quasi-periodic oscillations with periods ranging from about 1 to 108 s in all studied DPSs. This strongly supports the idea that DPSs are generated during a fragmented magnetic reconnection. Phases of most the oscillations in DPSs, especially for the period around 1 s, are synchronized ("infinite" frequency drift) in the whole frequency range of DPSs. For longer periods in some DPSs we found that the phases of the oscillations drift with the frequency drift in the interval from -17 to +287 MHz\s. We propose that these drifting phases can be caused (a) by the fast or slow magnetosonic waves generated during the magnetic reconnection and propagating through the plasmoid, (b) by a quasi-periodic structure in the plasma inflowing to the reconnection forming a plasmoid, and (c) by a quasi-periodically varying reconnection rate in the X-point of the reconnection close to the plasmoid.