This Letter presents the results of a search for a heavy particle decaying into an e±μ∓e±μ∓, e±τ∓e±τ∓, or μ±τ∓μ±τ∓ final state in pp collisions at √s=7 TeV. The data were recorded with the ATLAS detector at the LHC during 2011 and correspond to an integrated luminosity of 4.6 fb−14.6 fb−1. No significant excess above the Standard Model expectation is observed, and exclusions at 95% confidence level are placed on the cross section times branching ratio for the production of an R-parity-violating supersymmetric tau sneutrino. For a sneutrino mass of 500 (2000) GeV, the observed limits on the production cross section times branching ratio are 3.2 (1.4) fb, 42 (17) fb, and 40 (18) fb for the eμ, eτ, and μτ modes, respectively. These results considerably extend constraints from Tevatron experiments.