I was about to close your question as too broad, but then I found this peer-reviewed article which answers your question... by saying that it's too broad and vague :-)
Short version: there are too many pathologies clumped together in the RSI definition, and not enough studies have been done because of the vagueness.
Repetitive strain injury remains a controversial topic. The term repetitive strain injury includes specific disorders such as carpal tunnel syndrome, cubital tunnel syndrome, Guyon canal syndrome, lateral epicondylitis, and tendonitis of the wrist or hand. The diagnosis is usually made on the basis of history and clinical examination. Large high-quality studies using newer imaging techniques, such as MRI and ultrasonography are few. Consequently, the role of such imaging in diagnosis of upper limb disorders remains unclear. In many cases, no specific diagnosis can be established and complaints are labelled as non-specific. Little is known about the effectiveness of treatment options for upper limb disorders. Strong evidence for any intervention is scarce and the effect, if any, is mainly short-term pain relief. Exercise is beneficial for non-specific upper limb disorders. Immobilising hand braces and open carpal tunnel surgery release are beneficial for carpal tunnel syndrome, and topical and oral non-steroidal anti-inflammatory drugs, and corticosteroid injections are helpful for lateral epicondylitis. Exercise is probably beneficial for neck pain, as are corticosteroid injections and exercise for shoulder pain. Although upper limb disorders occur frequently in the working population, most trials have not exclusively included a working population or assessed effects on work-related outcomes.