We present the discovery of spectacular double X-ray tails associated with ESO 137-001 and a possibly heated X-ray tail associated with ESO 137-002, both late-type galaxies in the closest rich cluster Abell 3627. A deep Chandra observation of ESO 137-001 allows us for the first time to examine the spatial and spectral properties of such X-ray tails in detail. Besides the known bright tail that extends to ~80 kpc from ESO 137-001, a fainter and narrower secondary tail with a similar length was surprisingly revealed, as well as some intriguing substructures in the main tail. There is little temperature variation along both tails. The widths of the secondary tail and the greater part of the main tail also remain nearly constant with the distance from the galaxy. All these results challenge the current simulations. The Chandra data also reveal 19 X-ray point sources around the X-ray tails. We identified six X-ray point sources as candidates of intracluster ultra-luminous X-ray sources with L 0.3-10 keV of up to 2.5 × 1040 erg s–1. Gemini spectra of intracluster H II regions downstream of ESO 137-001 are also presented, as well as the velocity map of these H II regions that shows the imprint of ESO 137-001's disk rotation. For the first time, we unambiguously know that active star formation can happen in the cold interstellar medium (ISM) stripped by intracluster medium (ICM) ram pressure, and it may contribute a significant amount of the intracluster light. We also report the discovery of a 40 kpc X-ray tail of another late-type galaxy in A3627, ESO 137-002. Its X-ray tail seems hot, ~2 keV (compared to ~0.8 keV for ESO 137-001's tails). The Hα data for ESO 137-002 are also presented. We conclude that the high-pressure environment around these two galaxies is important for their bright X-ray tails and the intracluster star formation. The soft X-ray tails can reveal a great deal of the thermal history of the stripped cold ISM in mixing with the hot ICM, which is discussed along with intracluster star formation.