We have analyzed all the archival X-ray data of 134 unidentified (unID) gamma-ray sources listed in the first Fermi/LAT (1FGL) catalog and subsequently followed up by the Swift/XRT. We constructed the spectral energy distributions (SEDs) from radio to gamma-rays for each X-ray source detected, and tried to pick up unique objects that display anomalous spectral signatures. In these analyses, we target all the 1FGL unID sources, using updated data from the second Fermi/LAT (2FGL) catalog on the Large Area Telescope (LAT) position and spectra. We found several potentially interesting objects, particularly three sources, 1FGL J0022.2-1850, 1FGL J0038.0+1236, and 1FGL J0157.0-5259, which were then more deeply observed with Suzaku as a part of an AO-7 program in 2012. We successfully detected an X-ray counterpart for each source whose X-ray spectra were well fitted by a single power-law function. The positional coincidence with a bright radio counterpart (currently identified as an active galactic nucleus, AGN) in the 2FGL error circles suggests these sources are definitely the X-ray emission from the same AGN, but their SEDs show a wide variety of behavior. In particular, the SED of 1FGL J0038.0+1236 is not easily explained by conventional emission models of blazars. The source 1FGL J0022.2-1850 may be in a transition state between a low-frequency peaked and a high-frequency peaked BL Lac object, and 1FGL J0157.0-5259 could be a rare kind of extreme blazar.