Can different gauges of wire be used on the same circuit?

It is fine for the 15 amp circuits, but not for the 20 amp circuits.

The National Electrical Code requires circuits protected by a 20 amp circuit breaker to use #12 AWG copper wire throughout the circuit.

The National Electrical Code allows circuits protected by a 15 amp circuit breaker to use #12 AWG copper wire but #14 AWG wire cannot be protected by anything larger than a 15 amp breaker for power and lighting.

Regardless of where it is in the circuit, even if it is after the first receptacle, #14 wire cannot be used on a power or lighting circuit protected by a 20 amp breaker.

The following are pertinent excerpts from articles of the National Electrical Code:

210.20(B) Conductor Protection. Conductors shall be protected in accordance with 240.4.

240.4(D) Small Conductors. Unless specifically permitted in 240.4(E) or (G), the overcurrent protection shall not exceed that required by (D)(1) through (D)(7) after any correction factors for ambient temperature and number of conductors have been applied.

...

(3) 14 AWG Copper. 15 amperes

...

(5) 12 AWG Copper. 20 amperes

The #14 wire that is installed on 20 amp circuits would need to be replaced with #12 or the breaker on that circuit needs to be replaced by a 15 amp breaker.

Usually, 20 amp circuits are used for receptacle circuits and 15 amp circuits are used for lighting circuits.

Good luck!

It sounds like your father-in-law "reasoned things out" and "used his own judgement" rather than "blindly following" the "common practice" (in this case the electrical code). He was possibly thinking about the way water pipes (supply and drain) are sized. Unfortunately this does not work for home electrical systems. It actually works well under most normal operation, but fails if there is a combination of loads which allows close to 20 A to flow through the #14 conductors. A #14 copper conductor carrying 20 A would get very hot.

The immediate thing to do is to replace the 20-A breakers with 15-A breakers on any circuits which have any sections of 14 AWG copper wires. Then analyze the wiring and you would see that some circuits could be rewired to disconnect the 14 AWG part from the #12 and these all #12 sections could be upgraded to 20-A breakers. New #14 cables from 15-A breakers could then be installed to power the lights which are on #14.

You can always use a larger gauge than is required

So if you have a 15A circuit, you are required to use least 14 AWG wire. However if you want to use #12, #8, 4/0... whatever, as long as your wiring methods are proper.

There's one hitch, but it's a "practical, implementation" issue moreso than a rule. That's attaching the wire to the device, receptacle, switch, whatever, or making the larger wire fit somewhere.

For instance I just looked at a 15A receptacle, and it is listed for #12 or #14 copper wire -- and only #14 solid if using the backstab (which is a bad idea). You have to comply with all that. So if you upsized to #10, you can't connect it to that receptacle directly, you must pigtail the receptacle with a #12 (or possibly #14 if on a 15A circuit).

Or say you have 10 of these conductors to put down a 1/2" EMT conduit. That's legal with #12, but if you upsize to #10, that exceeds conduit fill rules.

And of course you still have to follow all the other circuit rules, so if you have a 20A socket, it still has to be on a 20A breaker even if the wire is #8.

If a 15 amp breaker is installed on a 12 gauge wire, any electrician should think the wire is a long run and not that it was incorrectly installed on a 15 amp breaker.

Before changing the 15 amp breaker to a 20 amp breaker, it is the responsibility of the electrician to make sure the entire circuit is run with a minimum wire size of 12 gauge.

Yes you can use on a 15 amp circuit breaker a 12 gauge wire from your panel to the first receptacle then continue with 14 gauge wire. It would in fact need to be done that way if your first receptacle requières a wire that was more than 50 feet long. Then, assuming the other receptacles would be in the vicinity of the first receptacle, a 14 gauge wire could be used to connect the rest of the receptacles