It depends upon what is the goal for your analysis. If you wish to better identify the strain, then molecular characterization is the most accurate. However if you wish to better know the phenotypes of the strains, then testing those is the most relevant.
Below genus level morphological identification is complicated, if not impossible in many cases. For sequences, check Fusarium-DB. TEF or IGS sequences are probably the best in this case. ITS may not discriminate between species within some complexes
I think you want to differentiate the Fusarium spp. upto species level. One thing you mentioned in your question that 50 strains this is culture or isolates. These may be same or different yet not known. Initially you can study their morphology, in malt extract agar plates, taxonomy- microscopic study (spore size) and go for ITS sequencing and their phylogeny construction. For more authentication you can go for RAPD and ITS-RFLP markers also. From all the three methods concluded to identify the exact one.