Hypothesis: The internal topology of soft nanoparticles - regular (ideal) vs disordered (realistic) networks - and its intrinsic deformability (degree of cross-linking) influences solvent permeability (uptake, invasive and mixing capacities) under interfacial confinement. Methodology: By means of large-scale molecular dynamics simulations we study nanogels at liquid-liquid (A-B) interfaces covering the whole range of cross-linking degrees and interfacial strengths. The nanogel permeability is analyzed with a grid representation that accounts for the surface fluctuations and adds to the density profiles the exact number of liquid particles inside the nanogel. Unlike in previous investigations, excluded volume interactions are considered for all the particles (monomers and liquids). Findings: Nanogel's permeability is intrinsically related to the particle deformability. Ideal networks show higher values of the total liquid uptake and the invasive capacity (A-particles in B-side and vice versa) than realistic networks, though differences vanish in the limit of rigid interfaces. Uptake and invasion are optimized at a cross-linking degree that depends on the interfacial strength, tending to similar to 15 - 20% for moderate and stiff interfaces. As the interfacial strength increases, the miscibility inside the nanogel is enhanced by a factor of up to 5 with respect to the bare interface, with the disordered networks providing a better mixing than their ideal counterparts. (C) 2020 Elsevier Inc. All rights reserved.