Choosing a flash for OM-D
Flash units that support all or part of Olympus TTL control
Also see Gary Ayton's extensive webpage on Olympus compatible flash
Third Party Flash Radio Triggers that work non TTL (just trigger, no power control)
Most work, even cheap ones from eBay. There will be exceptions.
A prolific flash review site giving information on many flash units and triggers of all types is flashhavoc
Third Party Flash Radio Triggers that allow remote power control and triggering but no TTL
The Yongnuo 560 TX flash controller with the Yongnuo 560 Mark III or Mark IV flash power control system.
Third Party Flash and Radio Triggers that allow remote power control and High Speed Sync
Profoto Air TTL and HSS compatibility with the Air Remote TTL-O
Elinchrom Skyport Plus HS for Olympus (wireless triggers are available for other brands of cameras to the Elinchrome studio flashes)
http://www.cactus-image.com/special/Cactus-V6II-HSS/ - read the manual (Cactus is a wireless trigger that allows your Olympus camera to trigger Olympus and other brands of flashes as well as Cactus brand flashes). Cactus and hot shoe fit issues on the E-M1)
Godox Flashpoint and Godox Flash System also described by TJ Houston - Godox allows your Olympus camera to control Godox brand flashes whether they have an Olympus hotshoe or other brand hotshoe.
Hahnel Viper TTL transmitter (manual) allows your Olympus camera to trigger Hahnell Viper TTL receivers and Hahnell Modus flashes
Hahnel Captur transmitter (manual) can trigger the shutter of your Olympus body and remote flashes (when they are equipped with Captur receivers).
How to use a shutter speed faster than the max flash shutter speed without HSS
Essentially, by trick or not, set the body shutter speed to faster than the max flash shutter speed
Get a powerful remote flash, set it to maximum power - this will force a long flash duration.
Trigger the remote - check how much of the frame will be comfortably covered.
Further info
Gary Ayton's article
Optical to radio remote control.
The Aoktec flash control system
Using legacy film era flash on modern digital bodies
Film era flash could trigger at voltages over 100 volts. These could fry modern digital bodies that can only handle a maximum of 6 or 20 volts.
Use a Wein SafeSync