We address the task of automatically grading the language proficiency of spontaneous speech based on textual features from automatic speech recognition transcripts. Motivated by recent advances in multi-task learning, we develop neural networks trained in a multi-task fashion that learn to predict the proficiency level of non-native English speakers by taking advantage of inductive transfer between the main task (grading) and auxiliary prediction tasks: morpho-syntactic labeling, language modeling, and native language identification (L1). We encode the transcriptions with both bi-directional recurrent neural networks and with bi-directional representations from transformers, compare against a feature-rich baseline, and analyse performance at different proficiency levels and with transcriptions of varying error rates. Our best performance comes from a transformer encoder with L1 prediction as an auxiliary task. We discuss areas for improvement and potential applications for text-only speech scoring.