I had a FX 8300, was a good cpu in it's day but it's 32ns tech is just not able to do what the new 12ns and 7ns tech CPU's can do. It just cannot process the info quick enough and then throw DDR3 RAM into the mix and there you have your bottle neck.
Overclocking the FX 8300 (is it the Vishera ?) which I have done is not a big help as they run very hot due to the voltage increase needed to get anything meaningful on what is already a power hungry CPU so you will need a very good cooler.
To compound that the MoBo you have will be pretty old and may well not be able to handle the stress of the overclock and blow the Virtual Memory Controller or something else like a RAM slot....
The GPU is also boarderline for this day and age but it is not the main problem YET.
All in all what is said above is true, if you want a smooth gaming experience on modern titles and even more so in Multiplayer online games then the only way is to upgrade to a Ryzen (at least Ryzen 5 or 7 not 3) platform with good fast DDR4 RAM. It will cost a few bucks but still cheaper than going the Intel route.
Also what monitor do you play on with which refreshrate? and at what resolution do you play. Even if it says 60fps and you notice the stutter then it is more than likely it is because it is 60 fps being displayed but because it takes the CPU and GPU so long to process the next frame it is displaying the same frame up to three or even four times before the next new one is shown so it's not 60 new frames FPS/second . Therefore it feels like 35-40 fps playing.
Cheers