Motivated by the report of the giant Rashba effect in ternary layered compounds BiTeX, we consider two Janus structured compounds Ti2N2XI (X = Br, Cl) of the same ternary family exhibiting a 1 : 1 : 1 stoichiometric ratio. Broken inversion symmetry in the Janus structure, together with its unique electronic structure exhibiting anti-crossing states formed between Ti-d states and strong spin-orbit coupled I-p states, generates large Rashba cofficients of 2-3 eV Å for these compounds, classifying them as strong Rashba compounds. The anti-crossing features of the first-principles calculated electronic structure also result in non-trivial topology, combining two quantum phenomena - Rashba effect and non-trivial topology - in the same materials. This makes Janus TiNI compounds candidate materials for two-dimensional composite quantum materials. The situation becomes further promising by the fact that the properties are found to exhibit extreme sensitivity and tunability upon application of uniaxial strain.