Why am I only getting 92V at receptacles?
When multiple things go out, find out what they have in common.

I'm making a couple of assumptions here, since you changed out one of the sockets, you understand that the breaker must be turned off in order to work on the circuit and that you are actually using a voltmeter to make sure the circuit is dead when the breaker is off before opening up any outlet box. That this is American wiring per NEC. Also that you are not dealing with aluminum wiring.


First step is the breaker, turn it off and push it fully to the off position to reset the internal mechanism. All items (lights &amp; sockets) on that circuit should die. Note what is unpowered on that circuit so you can verify later whether this is a full circuit or partial circuit power loss.
Turn the breaker back on and check the voltage on the breaker output in the breaker panel. If it's 92VAC there, the circuit breaker could have bad internal contacts (breaker needs to be replaced, don't mess with it if you aren't sure how to do it) or on some evilly constructed panels, the contacts to the bus bars may be bad (get an electrician IF THIS IS THE CASE, Buss bar erosion is a dangerous situation). Make sure the output lug on the circuit breaker has a tight connection.
If with the circuit breaker on, the same amount of items are are lacking power as were unpowered when the circuit breaker was off, you have an open connection in the wiring leading to the first socket in the daisy chain, or the incoming connection to the first socket is bad.
If only part of the items on the circuit come on when the breaker on, then you have a bad connection in a circuit daisy chain. When you look at intermediate sockets in the circuit, commonly a pair of wires carries power to the socket and another pair carries the power to the next socket in the chain. Find the first socket in the circuit, check voltage down the chain till you find the drop. The bad connection will be either the last socket with full power or the first one that shows the voltage drop.


Depending on the era and the electrician, the daisy chain may be continued by: 


Wire-nutting the two cables (black to black, white to white) and running a pigtail from each to the appropriate socket connection.
By connecting one cable to a pair of hot and neutral screws (black/hot to brass, white/neutral to silver) and continuing the power to the next item in the chain from the second set of screws (newer sockets also allow for straight stripped wire going under a plate that's tightened by the screws)
By using the push-in connections on the socket in a similar configuration


My experience with a broken chain causing partial circuit power loss is with an electrician using the push-in connectors. 

The failure was due to poor contact and heating that melted the first or second socket because these two sockets have to carry all or almost all the current in the circuit and if the wires don't enter the push-in straight or have burrs that don't allow them to seat properly you get a loose contact that gets worse over time. Heating anneals the brass and the spring contact goes away.

I haven't seen a screw tightened copper wire connection do that yet, they seem to have a larger surface area and are mechanically tightened instead of depending on spring contact.

I have seen burned aluminum screw contacts where there was a mismatch (non-CO/ALR) and bad assembly, that's another scary situation that opens up a whole 'nother can of worms.

NOTE: Grounding was ignored in the above discussion, bare wire goes to green screw ground lug, wire nut with pigtail is handy for this.