We present numerical simulation studies of the steady-state magnetization dynamics driven by a spin-polarized current in a point contact geometry for the case of a relatively large contact diameter (D = 80 nm) and small external field (H = 30 Oe). We show, that under these conditions the magnetization dynamics is qualitatively different from the dynamics observed for small contacts in large external fields. In particular, the 'bullet' mode with a homogeneous mode core, which was the dominating localized mode for small contacts, is not found here. Instead, all localized oscillation modes observed in simulations correspond to different motion kinds of vortex-antivortex (V-AV) pairs. These kinds include rotational and translational motion of pairs with the V-AV distance d ~ D and creation/annihilation of much smaller (satellite) V-AV pairs. We also show that for the geometry studied here the Oersted field has a qualitative effect on the magnetization dynamics of a 'free' layer. This effect offers a possibility to control magnetization dynamics by a suitable electric contact setup, optimized to produce a desired Oersted field. Finally, we demonstrate that when the magnetization dynamics of the 'fixed' layer (induced only by the stray field interaction with the 'free' layer) is taken into account, the threshold current for the oscillation onset is drastically reduced and new types of localized modes appear. In conclusion, we show that our simulations reproduce semiquantitatively several important features of the magnetization dynamics in a point contact system for low external fields reported experimentally.