We present a comprehensive analysis of the multi-phase structure of the interstellar medium (ISM) and the stellar kinematics in the edge-on nearby galaxy UGC 10205 using integral field spectroscopy (IFS) data taken with MEGARA at the GTC. We explore both the neutral and the ionized gas phases using the interstellar Na ${small I}$ D doublet absorption (LR$-$V set-up, R $sim$ 6000) and the H$alpha$ emission line (HR$-$R set-up, R $sim$ 18000), respectively. The high-resolution data show the complexity of the H$alpha$ emission line profile revealing the detection of up to three kinematically distinct gaseous components. Despite of this fact, a thin disk model is able to reproduce the bulk of the ionized gas motions in the central regions of UGC 10205. The use of asymmetric drift corrections is needed to reconciliate the ionized and the stellar velocity rotation curves. We also report the detection of outflowing neutral gas material blueshifted by $sim$ 87 km s$^{-1}$. The main physical properties that describe the observed outflow are a total mass M$_{out}$ $=$ (4.55 $pm$ 0.06) $times$ 10$^{7}$ M$_{odot}$ and a cold gas mass outflow rate $dot{M}$$_{out}$ $=$ 0.78 $pm$ 0.03 M$_{odot}$ yr$^{-1}$. This work points out the necessity of exploiting high-resolution IFS data to understand the multi-phase components of the ISM and the multiple kinematical components in the central regions of nearby galaxies.