OK,
There is a few items here that can be answered.
1. Solid #14 for powering your devices will not violate any robot rules. That size of solid wire is more like a crowbar to the connectors though. What vibration the wire will receive will be transmitted into the connector. I am afraid early connector failure will be the result.
2. There are a variety of outlets for wire. We use MCM Electronics for a variety of wire, parts and tools. You can find them at
http://www.mcmelectronics.com/
3. The Wago connectors do take solid wire but tinned, stranded wire is not the same. When you tin stranded wire, it does make the wire solid but in doing so, the outside strands cause a 'high spot' on the wire. These are what is contacting the the metal inside the connector and so all current must flow through these little spots on the outside of the wire. That increases the series resistance of the contact significantly. If you need to tin for making insertion easy, you can just add a little solder to the very end of the wire. The Wago connectors depend on this contact. If you really check into the specs, you will find that Wago downgrades the contact max current rating when used with solid wire simply due to the smaller contact area with solid wire. If you use the Wago ferrules, they are actually square in shape to maximize the contact area.