Interactive Voice Response (IVR) is a technology that allows automatic human-computer interactions, via a telephone keypad or voice commands. The systems are widely used in many industries, including telecommunications and banking. Virtualization is a potential technology that can enable the easy development of IVR applications and their deployment on the cloud. IVR virtualization will enable efficient resource usage by allowing IVR applications to share different IVR substrate components such as the key detector, the voice recorder and the dialog manager. Resource management is part and parcel of IVR virtualization and poses a challenge in virtualized environments where both processing and network constraints must be considered. Considering several objectives to optimize the resource usage makes it even more challenging. This paper proposes IVR virtualization task scheduling and computational resource sharing (among different IVR applications) strategies based on genetic algorithms, in which different objectives are optimized. The algorithms used by both strategies are simulated and the performance measured and analyzed.