If you keep the USB strips adjacent and as short and neat as possible and you'll likely have no problems for a prototype.

For USB low speed, the 1.5Mbps is so low that you don't really need to put any effort into the routing. Even USB full speed at 12Mbps is pretty forgiving.

In terms of cable to board, cables with USB connectors on one end and 0.1" pitch headers on the other end are cheap and readily available, so that would solve trying to connect to the strip board. Alternatively a USB B connector has a pitch and shape that it is possible to install them on strip board.

If you keep the USB strips adjacent and as short and neat as possible and you'll likely have no problems for a prototype.

For USB low speed, the 1.5Mbps is so low that you don't really need to put any effort into the routing. Even USB full speed at 12Mbps is pretty forgiving.

In terms of cable to board, cables with USB connectors on one end and 0.1" pitch headers on the other end are cheap and readily available, so that would solve trying to connect to the strip board. 

Alternatively right-angle USB B connectors have a pitch and shape that it is possible to install them on strip board with a little care. From the image below, the 2.5mm pitch is close enough, holes can be drilled out for the 12.04mm mount spacing (close enough to 12.7mm) and the pins can be bent enough that the 2mm/2.71mm can become 2.54/2.54mm.

^{From Wurth 61400416121 Datasheet}

Even right-angle USB A connectors are close enough to be strip-board friendly.

^{From Wurth 61400416021 Datasheet}