Amblyopia, also known as lazy eye, affects 2-3% of children. If ambylopia is not treated successfully during early childhood, it will persist into adulthood. One of the causes of amblyopia is strabismus, which is a misalignment of the eyes. In this paper, we have investigated several neural network architectures as universal feature extractors for two tasks: (1) classification of eye images to detect strabismus, and (2) detecting the need to be referred to a specialist. We have examined several state-of-the-art backbone architectures for feature extraction, as well as several classifier frameworks. Through these experiments, we observed that VGG19 and random forest classifier offer the overall best performance for both classification tasks. We also observed that when top-performing architectures are fused together, even with simple rules such as a median filter, overall performance improves.