Quaternary III-V semiconductors are one of the most promising material classes in optoelectronics. The bandgap and its character, direct or indirect, are the most important fundamental properties determining the performance and characteristics of optoelectronic devices. Experimental approaches screening a large range of possible combinations of III- and V-elements with variations in composition and strain are impractical for every target application. We present a combination of accurate first-principles calculations and machine learning based approaches to predict the properties of the bandgap for quaternary III-V semiconductors. By learning bandgap magnitudes and their nature at density functional theory accuracy based solely on the composition and strain features of the materials as an input, we develop a computationally efficient yet highly accurate machine learning approach that can be applied to a large number of compositions and strain values. This allows for a computationally efficient prediction of a vast range of materials under different strains, offering the possibility of virtual screening of multinary III-V materials for optoelectronic applications.