Results. Using the LIRIS observations of the field T dvvarfs, we calibrated this imager for T spectral typing via methane photometry. The three S On objects were spectroscopically classified as T4.5 +/- 0.5 (S On 73), T5 +/- 0.5 (S On J053804.65-021352.5). and T7+7,1 (S On 70). These spectral types agree with the measured H-band methane colors. The similarity between the observed JH spectra and the methane colors and the data of field ultra cool dwarfs of related classifications suggests that S On 70, 73, and S On J053804.65-021352.5 do not deviate significantly in surface gravity in relation to the field. Additionally, the detection of K at similar to 1.25,um in S On J053804.65-021352.5 points to a high-gravity atmosphere. Only the K-band reddish nature of S On 70 may be consistent with a low gravity atmosphere. The proper motions of S Ori 70 and 73 are measurable and are larger than that of the cluster by >3.5 sigma. The proper motion of S On J053804.65-021352,5 is consistent with a null displacement. These observations suggest that none of the three T dwarfs is a likely sigma Orionis member, and that either planetary-mass objects with masses below: similar to 4 M-JUP, may not exist free-floating in the cluster or they may lie at fainter near-infrared magnitudes than those of the targets (i.e., H > 20.6 rnag). thus remaining unidentified to date. We determined the volume density of field T4-T7 dwarfs to be >= 2.8 +/- 1.6 x 10(-3) pc(-3) from a survey that covered 2798.4 arcmin(2) and was complete up to a distance of 119 pc.