It helps to know the router you are using. However, in general this is how to make it work.
First, wireless print servers are troublesome. If you can locate both of the printers near your router and use a hardwired connection to connect them to the network, that would be the preferred connection.
Second, HP’s branded print servers are the most reliable with their printers. Although pricey if you pay retail, they are available from eBay and the internet at substantial discounts (as much as 60-90% discount)
The way it works is you connect a print server to each of the printers and connect that to the router via ethernet cable or, in the case of a wireless print server, the wireless network. Usually there is an install disc that creates a tcp/ip port for the printer to print to and adds it to the list of installed printers.
The print servers compatible with the 1020 are
HP Jetdirect ew2400 (J7951a)
HP Jetdirect en3700 (J7942a)
HP Jetdirect 175x (J6035c)
For the 1319 MFP I don’t get any network information. I’m guessing the faxing and scanning across the network are not supported but printing probably is. A call to HP tech support will likely give you some direction.
You can try other brands of print servers, but the results are not guaranteed.
I am grateful, thank you.