Looking for the right LED driver, roughly 4V, 1.5W or 3W, 10-20Hz
I would use a LM555; it's a very flexible, cheap, and easy-to-find timer chip. And you can find lots of examples on how to use it. Here's one to start with. The 555 will source around 125mA, which isn't quite enough for your application. If want to drive all of the strings at once, you can do it with an NPN transitor switch hooked to the output of the 555. I would probably start with a TIP120; that's hefty enough to handle the current you need to switch. You will need a way to power all of the strings at once. If you are using batteries, I would use 3 D cells to drive all of the strings. If you are okay with a plug-in solution, you can find lots of small wall wart power supplies that put out 5V at 1Amp; they are used to charge cell phones and other kinds of electronigs