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On-chip implementation of optical nonlinear activation functions (NAFs) is essential for realizing large-scale photonic neural chips. To implement different neural processing and machine learning tasks with optimal performances, different NAFs are explored with the use of different devices. From the perspective of on-chip integration and reconfigurability of photonic neural network (PNN), it is highly preferred that a single compact device can fulfill multiple NAFs. Here, we propose and experimentally demonstrate a compact high-speed microdisk modulator to realize multiple NAFs. The fabricated microdisk modulator has an add-drop configuration in which a lateral PN junction is incorporated for tuning. Based on high-speed nonlinear electrical-optical (E-O) effect, multiple NAFs are realized by electrically controlling free-carrier injection. Thanks to its strong optical confinement of the disk cavity, all-optical thermo-optic (TO) nonlinear effect can also be leveraged to realize other four different NAFs, which is difficult to be realized with the use of electrical-optical effect. With the use of the realized nonlinear activation function, a convolutional neural network (CNN) is studied to perform handwritten digit classification task, and an accuracy as large as 98% is demonstrated, which verifies the effectiveness of the use of the high-speed microdisk modulator to realize the NAFs. Thanks to its compact footprint and strong electrical-optical or all-optical effects, the microdisk modulator features multiple NAFs, which could serve as a flexible nonlinear unit for large-scale PNNs.