Properties of point defects resulting from the incorporation of inert-gas atoms in bcc tungsten are investigated systematically using first-principles density functional theory (DFT) calculations. The most stable configuration for the interstitial neon, argon, krypton and xenon atoms is the tetrahedral site, similarly to what was found earlier for helium in W. The calculated formation energies for single inert-gas atoms at interstitial sites as well as at substitutional sites are much larger for Ne, Ar, Kr and Xe than for He. While the variation of the energy of insertion of inert-gas defects into interstitial configurations can be explained by a strong effect of their large atomic size, the trend exhibited by their substitutional energies is more likely related to the covalent interaction between the noble gas impurity atoms and the tungsten atoms. There is a remarkable variation exhibited by the energy of interaction between inert-gas impurities and vacancies, where a pronounced size effect is observed when going from He to Ne, Ar, Kr, Xe. The origin of this trend is explained by electronic structure calculations showing that p-orbitals play an important part in the formation of chemical bonds between a vacancy and an atom of any of the four inert-gas elements in comparison with helium, where the latter contains only 1s2 electrons in the outer shell. The binding energies of a helium atom trapped by five different defects (He-v, Ne-v, Ar-v, Kr-v, Xe-v, where v denotes a vacancy in bcc-W) are all in excellent agreement with experimental data derived from thermal desorption spectroscopy. Attachment of He clusters to inert gas impurity atom traps in tungsten is analysed as a function of the number of successive trapping helium atoms. Variation of the Young modulus due to inert-gas impurities is analysed on the basis of data derived from DFT calculations.