Using two signal generators with inverters to create 180 degree phase shifts can be an option depending on the timing specifications you are looking to achieve. You mentioned you want the four signals to be synchronized. The inverters may introduce some propogation delay and possibly other non-ideal characteristics that can affect how well the signals are synchronized. The magnitude of these effects is dependent on the specifications of the inverters. Using 4 signal generators, you could ensure that all four signals are generated simultaneously (within the specifications of one of our methods for synchronization) wihout having to deal with any delays introduced by the inverters.
Synchronizing multiple PXI/PCI cards in one chassis can be done in several different ways. I have included some documents below that should give you a good overview of your options and how they can be implemented. The 5412's support T-Clock synchronization so I have also included a link to the Help documentation on this subject.
As far as training goes, our website is a valuable resource for tutorials and examples that can help you learn more on how to program in LabVIEW to control the signal generators. The driver for signal generators, NI-FGEN, also comes with a lot of example code that can help you get started. I have included another link to a page contained in the Developer Zone of our website that has a list of video demos on several different topics related to signal generators.