The isoscalar E1 and E2 resonances in the proton-rich nuclei ^48,49Ni and the {f_7/2⊗ 3^-} multiplet in ⁴⁹Ni have been calculated taking into account the single-particle continuum exactly. The analogous calculations for the mirror nuclei ⁴⁸Ca and ⁴⁹Sc are presented. The models used are the continuum random-phase approximation (RPA) for ⁴⁸Ni, ⁴⁸Ca and the odd RPA for ⁴⁹Ni, ⁴⁹Sc, where the latter has been developed recently and describes both single particle and collective excitations of an odd nucleus on a common basis. In all four nuclei, we obtained a distinct splitting of the isoscalar E1 resonance into 1hω and 3hω peaks at about 11 MeV and 30 MeV, respectively. The main part of the isoscalar E1 energy-weighted sum rule (EWSR) is exhausted by the 3hω resonances. The 1hω resonances exhaust about 35% of this EWSR in ^48,49Ni and about 22% in ⁴⁸Ca and ⁴⁹Sc. All seven {f_7/2⊗ 3^-} multiplet members in ⁴⁹Ni are calculated to be in the 6-8 MeV energy region and have noticeable escape widths.