Images shared on social media help crisis managers gain situational awareness and assess incurred damages, among other response tasks. As the volume and velocity of such content are typically high, real-time image classification has become an urgent need for faster disaster response. Recent advances in computer vision and deep neural networks have enabled the development of models for image classification for a number of tasks, including detecting crisis incidents, filtering irrelevant images, classifying images into specific humanitarian categories, and assessing the severity of the damage. To develop robust models, it is necessary to understand the capability of the publicly available pretrained models for these tasks, which remains to be underexplored in the crisis informatics literature. In this study, we address such limitations by investigating ten different network architectures for four different tasks using the largest publicly available datasets for these tasks. We also explore various data augmentation strategies, semisupervised techniques, and a multitask learning setup. In our extensive experiments, we achieve promising results.