Massive stars severely influence their environment by their strong ionizing radiation and by the momentum and kinetic energy input provided by their stellar winds and supernovae. Quantitative analyses of massive stars are required to understand how their feedback creates and shapes large scale structures of the interstellar medium. The giant HII region N 206 in the Large Magellanic Cloud contains an OB association that powers a superbubble filled with hot X-ray emitting gas, serving as an ideal laboratory in this context. We aim to estimate stellar and wind parameters of all OB stars in N 206 by means of quantitative spectroscopic analyses. In this first paper, we focus on the nine Of-type stars located in this region. We determine their ionizing flux and wind mechanical energy. The analysis of nitrogen abundances in our sample probes rotational mixing. We obtained optical spectra with the multi-object spectrograph FLAMES at the ESO-VLT. When possible, the optical spectroscopy was complemented by UV spectra from the HST, IUE, and FUSE archives. Detailed spectral classifications are presented for our sample Of-type stars. For the quantitative spectroscopic analysis we used the Potsdam Wolf-Rayet model atmosphere code. We determined the physical parameters and nitrogen abundances of our sample stars by fitting synthetic spectra to the observations. The stellar and wind parameters of nine Of-type stars, which are largely derived from spectral analysis are used to construct wind momentum - luminosity relationship. We find that our sample follows a relation close to the theoretical prediction, assuming clumped winds. The most massive star in the N 206 association is an Of supergiant that has a very high mass-loss rate. Two objects in our sample reveal composite spectra, showing that the Of primaries have companions of late O subtype. All stars in our sample have an evolutionary age of less than 4 million yr, with the O2-type star being the youngest. All these stars show a systematic discrepancy between evolutionary and spectroscopic masses. All stars in our sample are nitrogen enriched. Nitrogen enrichment shows a clear correlation with increasing projected rotational velocities. The mechanical energy input from the Of stars alone is comparable to the energy stored in the N 206 superbubble as measured from the observed X-ray and H{alpha} emission.