During the interval from 06:15 to 07:30 UT on 24 August 2005, the Chinese Tan-Ce 1 (TC1) satellite observed the multiple responses of the near-Earth magnetotail to the combined changes in solar wind dynamic pressure and interplanetary magnetic field (IMF). The magnetotail was highly compressed by a strong interplanetary shock because of the dynamic pressure enhancement (similar to 15 nPa), and the large shrinkage of magnetotail made a northern lobe and plasma mantle move inward to the position of the inbound TC1 that was initially in the plasma sheet. Meanwhile, the dynamic pressure fluctuations (similar to 0.5-3 nPa) behind the shock drove the quasi-periodic oscillations of the magnetopause, lobe-mantle boundary, and geomagnetic field at the same frequencies: one dominant frequency was around 3 mHz and the other was around 5 mHz. The quasi-periodic oscillations of the lobe-mantle boundary caused the alternate entries of TC1 into the northern lobe and the plasma mantle. In contrast to a single squeezed or deformed magnetotail by a solar wind discontinuity moving tailward, the compressed and oscillating magnetotail can better indicate the dynamic evolution of magnetotail when solar wind dynamic pressure increases and fluctuates remarkably, and the near-Earth magnetotail is quite sensitive even to some small changes in the solar wind dynamic pressure when it is highly compressed. Furthermore, it is found that a considerable amount of oxygen ions (O(+)) appeared in the lobe after the southward turning of IMF.