Could be your router, but it's probably a problem with the signal.
If you're using a wireless router, there may be too much interference. (Check your signal strength)
Regarding the wired setup, your plugs may be poorly attached to your cables or your cables could be damaged.
Perhaps your router is just bad (not the most likely option).
Or maybe the actual signal that comes into your house from your ISP is just poor.
Try and log into your router and see if you can find a statistics page where you can see what actual speed you are connected at (of the 20/1.5) and how much packet loss it lists. Cheap routers will probably not have such a page.