This study aimed to maximise the content of water-soluble protein (WSP) and β-glucan (BG) in oat drink (OD) products by optimising the duration of treatment with neutral (NP) and acidic (AP) proteases. Additionally, it investigated the correlation between changes in the OD's nutritional profile and its rheological and sensory properties. After initial treatment with α-amylase, the OD samples were divided into two groups, i.e., one treated with NP and the other with AP for 30, 60, 120, and 180 min. The samples were then analysed for their WSP and BG contents. Samples with an optimised treatment duration were evaluated for their rheological and sensory properties. The OD sample treated with AP for 60 min exhibited the highest β-glucan (0.52 g/100 mL) and WSP (1.56 g/100 mL) contents, improved storage stability, and the lowest sedimentation rate (2.13%/h), compared to the control OD sample. However, sensorially, this sample was characterised by a sticky, gluey mouthfeel and was less acceptable as a drinkable product. This study demonstrated the potential effect of protease treatment on enhancing the nutritional value and stability of OD products, although further studies are necessary to improve the sensory properties of these drinks.