This is all drawn from the mostly canon tie in novel trilogy, The Passing of the Techno-mages. Much of this would have been part of the sequel series Crusade, if that show had continued.
There's the story the mages have...
"We entertain, we enlighten, but what power do we truly possess? The mages of old, the Taratimude, they had power. And they used it wisely, decisively. They knew how to make the tech, and how to use it. We've lost so much..." Elizar to Galen, Casting Shadows Chapter 3
The mages were founded by an avian race called the Taratimude. Their race had invented a set of body implants that combined biomechanical and more traditional technology. The implants thread through the entire body and join with a mage's central nervous system, and through some technobabble, draws energy from the universe itself. That energy can be directed by the mage into a great many effects, including shields, illusions, physical force, healing, and attacks (if needed). This is in addition to more basic benefits like enhanced healing for their bodies, sensor and scanning abilities, and a completely integrated computer and communications system embedded in. The Taratimude are long gone in an ancient catastrophe, but the mages are still able to duplicate their implants for new mages, even if they don't understand them. The implants are usually simply referred to as "the tech".
The technomages are capable of rather wondrous things with their implants. The energy projections or illusions can be complete enough to mimic reality, although they do tend to have a range limited mostly to line of sight. They can conjure moving floating platforms to levitate or fly, or add physical aspects to their illusions. Although they cannot reverse-engineer their implants, they have used them to craft their own technology, to create ships, tools of magic, and places of power.
They have trained themselves in the art of controlling perceptions, much like traditional magicians, and so often they appear capable of much more, or can work completely disguised (they cannot teleport; Elric was putting on a good show for Vir). To assist this magical aspect, they have developed their own audio/visual bugs that verge on the microscopic, and their hacking skills to access existing databases and security systems probably cannot be beat. Between the two, they can feed endless information to their internal computers, and analyze that information so quickly that they can appear near-omniscient. Add in silent and instant communication, and a team of mages can be so thorough in their manipulations that a mark can never realize they were being manipulated at all.
...and then there's the truth.
"Why don't you kill me?"
"Because you are already one of us."
Galen and Morden, Casting Shadows, Chapter 15
The "tech" is, and always has been, Shadow tech. This is the most closely guarded secret of the mages, only known to members of the Circle that lead them.
The Shadows developed the tech as part of a "super soldier" program. The original functions embedded within were energy projections for things like laser weaponry, spheres of imploding space, and body armor, among others. The implants also agitated the user, filling them with a sense of energy and need for action, encouraging temper and anger, the better to spread chaos with. The Taratimude were simply the first race to accept the implants.
The project worked a little too well. The Taratimude acted as commandos in the Shadow's ground forces, and wreaked havoc. In the long run, however, the agitation of the implants encouraged them to start taking out their anger on anything in range, or on their fellows. These implants had no ability to override a sentient mind as with Shadow capital ships, just some basic kill switches, so the Taratimude went wild. Some few that had better control survived the catastrophe, escaped to a new world, and founded the order of the technomages. They began by stressing training and control over the tech to fight the Shadow impulses, and twisting the combat functions into something more benign. Over time, knowledge of the original purpose of the "tech" was lost to the mages, and so was knowledge of the original functions that made them such lethal tools.
The Shadows decided they wanted control of their weapons more than pure chaos, and abandoned the project, apart from tracking down and locating their errant group of shock troops for one last purpose. Their leader, Wierden, was captured and taken back to Z'ha'dum to be used as part of a different project.
The technomages did not, and have never had, the ability to duplicate the tech, nor the will or lack of morals to even if they knew how (it involves using other sentients, and is quite icky). The servants of the Shadows, under orders, have continued to secretly supply the order with the original implants so they can initiate new members. The Shadows appear to have done this believing the technomages could be recruited, or turned to their own purposes later - at minimum, they should pose no direct threat to the Shadows and be a source of ... spare parts, much like Wierden was, and at maximum, they could fall to their base impulses and serve the cause of chaos. This is the reason for their flight from known space - the Shadows were already recruiting mages, and making examples of those that refused or knew too much.