I've not looked at this for years, so take the below as meandering thoughts:
1) Unless you want to make a deep study of this stuff, I'd recommend looking for 'review articles' in well respected journals. Trying to look at individual studies will drive you crazy. As part of a statistics course, I remember a review article in "The Mathematical Intellegencer" sometime around 1990. I am certain that there will be more recent works!
2) If there are real dangers from EMF, they are still very low risk dangers. For example, if you _double_ the risk of an extremely rare disease, it is _still_ extremely rare. Because the risks are so small, it takes very extensive studies to separate the real risks from simply random noise and variation.
3) One of the studies that I do remember was of telephone company workers. The workers we divided into three groups: low exposure (billing people), medium exposure (primarily outside line workers), and high exposure (switching office workers). The group that showed a significant risk increase: the medium exposure group. The theory was that the outside line workers were being exposed to _chemicals_, eg transformer PCBs while doing their work, and that this totally swamped any risk difference cause by the EMF exposure. IMHO before worrying about the spooky 'EMFs', it is more important to be on the lookout for known real dangers at the locations you are working in. Do these constant current transformers use insulating oil? Is it known to be PCB free?
4) One oft repeated chestnut is that the energy levels associated with EMF are too low to cause cellular damage associated with cancer and other diseases. This is true. To break bonds associated with DNA, you need high energy photons or particulate radiation (x-rays, neutrons, etc.) There is no way that electrical power EMF can get to these energy levels unless you have such high total flux levels that you get actual _heating_ (yes, a big enough 60 Hz field won't produce photons that break DNA, but it could heat you enough that you _cook_). My _guess_ is that as research uncovers the real issues, they will find the connection between EMF and harm comes about through unexpected links.
-Jon