Eth cord port to big for wall port

Sounds like the wall port is an RJ-11 (6 pins for up to phone 3 lines, usually not all present/connected) phone port.  Ethernet only comes in one size (RJ45, 8 pins) unless you're talking fiber or some sort of connector you don't normally see outside of a datacenter, and those don't look like a standard ethernet port/plug.  RJ11 and RJ45 look very similar except that RJ45 is larger and has two more wires.  Old RJ45 wiring may not have all the pins connected, but still uses the same connector.  If such old wiring was done correctly at the time it will still work for ethernet but will not support 1Gb speed or higher and will be limited to 10 or 100Mb.

What are you trying to plug into the wall?  Are you trying to connect a Cable router or modem to existing wiring and a computer on the other end?

There are devices that allow you to run a network over phone wiring.  There are also devices for running a network over coaxial cables (MOCA) or electrical wiring.  The Coaxial/MOCA ones work really well for point-to-point runs, but they slow down if you have branches with splitters and multiple MOCA adapters.  For the fastest network you'll probably have to pull new cables, but most people don't do that and just use WiFi unless they have performance problems with WiFi.  What you should do really depends on the building and what you want to achieve in terms of network performance.  If you're not sure what you want to achieve, what service speed do you have?  People tend to want to be able to "get what they're paying for" on a speed test.