I am wondering would router wifi signal strength drop significantly when large number of users connecting onto it? Or is there any possible problems could arise when there is a sudden surge of large volume of people trying to connect to a single router?
The medium for wireless communication is air/space which is limited. There is only so much of it. The more clients connecting the more medium is used less medium there is for others. The signal strength would not really be compromised. The signal strength depends on the room parameters (humidity, type of walls, other radio frequencies in operation). There is a limited amout of clients that can connect. The limit is generally bound to the specs of the access point, but in essence would be limited to the amount of available bandwidth/space in the air within that given frequency. So I think to answer your question, the more users connecting to an access point the less performance in general you can expect, this resulting because of shared bandwidth/medium (space). Signal strength is more of a constant, how far that signal gets or how many clients your access point can serve is based on other factors.
A starting point is that signal strength really isn't the issue, it's the signal-to-noise ratio. A wi-fi radio is listening to one transmission at a time. If energy from another transmission comes in it can make the decoding the initial reception more difficult. The ability to decode is based upon SNR and not the received power.
To make it possible for a radio to receive only one signal at a time, wi-fi uses something called collision avoidance (which is much different than wired ethernet's collision detect) so there is only one transmission to an AP's radio (or, more preciesly, a receiver's radio) at a time. (Note: APs these days have multiple radios so they can support things like 2.4G and 5G simultaneously and some have more) The avoidance techniques cause a bottleneck per distributed access to a shared medium, which is roughly 10K transmissions opportunities (TXOPs) per second at a peak. As more devices come in these TXOPs will be consumed.
Optimal avoidance techniques depend upon hearing peer transmissions in order not to clobber them. For wi-fi, there can be hidden nodes, i.e. two devices can hear the AP but not each other hence the potential to "interfere" with a current reception. In this case, a transmission can require more TXOPs so the AP can effectively reserve air time for the devices which can't hear one another.
So there is a performance impact of a sudden surge of devices but it's mostly due to the need to arbitrate for the AP's "ear." A way around this is to weaken the signal (cell coverage) and add more APs creating more cells, effectively increasing the number of simultaneous conversations that can be supported by the network.