Can I contribute to my employers 457 plan and my self-employed 401k?
Yes. See information Letter 2001-0232. In this letter the IRS details that for years beginning after December 31, 2001, an individual may be able to defer up to the maximum amount ($19,000 for 2019) to an IRC Sec. 457 plan and also defer the maximum amount ($19,000 for 2019) to a 401(k) plan. A solo 401k plan is a type of 401k plan but for the self-employed, so the same holds true.