Higher order mode based beam and cavity diagnostics in 1.3 GHz superconducting cavities at FLASH At the Free Electron Laser in Hamburg (FLASH) and the European X Ray Free Electron Laser superconducting TeV energy superconducting linear accelerator (TESLA) type cavities are used for the acceleration of electron bunches generating intense free electron laser (FEL) beams. A long rf pulse structure allows one to accelerate long bunch trains which considerably increases the efficiency of the machine. However intrabunch train variations of rf parameters and misalignments of rf structures induce significant trajectory variations that may decrease the FEL performance. The accelerating cavities are housed inside cryomodules which restricts the ability for direct alignment measurements. In order to determine the transverse cavity position we use a method based on beam excited dipole modes in the cavities. We have developed an efficient measurement and signal processing routine and present its application to multiple accelerating modules at FLASH. The measured rms cavity offset agrees with the specification of the TESLA modules. For the first time the tilt of a TESLA cavity inside a cryomodule is measured. The preliminary result agrees well with the ratio between the offset and angle dependence of the dipole mode which we calculated with eigenmode simulations.