  Excited states in $^{58,60,62}$Ni were populated via inelastic proton
scattering at the Australian National University as well as via inelastic
neutron scattering at the University of Kentucky Accelerator Laboratory. The
Super-e electron spectrometer and the CAESAR Compton-suppressed HPGe array were
used in complementary experiments to measure conversion coefficients and
$\delta(E2/M1)$ mixing ratios, respectively, for a number of $2^+ \rightarrow
2^+$ transitions. The data obtained were combined with lifetimes and branching
ratios to determine $E0$, $M1$, and $E2$ transition strengths between $2^+$
states. The $E0$ transition strengths between $0^+$ states were measured using
internal conversion electron spectroscopy and compare well to previous results
from internal pair formation spectroscopy. The $E0$ transition strengths
between the lowest-lying $2^+$ states were found to be consistently large for
the isotopes studied.
