I'd like to predicate this by saying that it is, by definition, impossible to have completely accurate statistics on incidents of something like voter fraud, since voter fraud done "well" is undetected.
I'll also use some data taken from the Heritage Foundation, since they have conducted the majority of the studies on voting fraud. The Heritage Foundation receives a large portion of its funding from organizations who want to prove voter fraud, so I feel that it is important that conclusions be held until a second, independent study verifies their statistics. That being said, here's what I found for the 2016 election.
Oregon reported 24 total cases of voter fraud in the 2016 election, with the majority of those cases involving someone voting in two states by casting two ballots. Some sources report 54, but I'm trying to report per the actual states publishing, as that (hopefully) minimizes bias. The Heritage Foundation did not have any statistics in Oregon for election fraud.
I could not find any statistics on voting fraud in Hawaii. Hawaii is a little bit unique, in that it is sufficiently isolated as to make obtaining this data difficult. The Heritage Foundation reported one civil case involving a woman claiming improper residency, which is not really related to vote by mail.
Colorado reported up to 48 cases of voter fraud in 2016, 10 of which involved one individual casting two ballots, the rest involving someone voting in multiple states. The only incident of Election Fraud reported by the Heritage Foundation in 2016 was for someone improperly forging signatures for an anti-fracking initiative to get it on the ballot. This is not related to vote by mail.
Washington reported 74 cases of possible voter fraud in 2016, 70 of which were prosecuted. The Heritage Foundation had no statistics on Washington for 2016.
The Government Accountability Institute released a 2017 study of voter rolls in 21 states from the 2016 election, accounting for 17% of all possible combinations of interstate voting, looking specifically at duplicate votes between states (easiest to accomplish through vote by mail per the above). They established just under 8500 cases as an estimate for total duplicate voter fraud across those 17 states. Per the study, this is out of a population of 75 million general election voters, establishing a reliable base estimate of 0.0113% voter fraud by duplicate votes.
The populations of Oregon, Colorado, and Washington (the only states where I found statistics for voter fraud) are 4.09 million, 5.54 million, and 7.3 million, respectively. Using the voter fraud data from earlier, these states have an estimated voter fraud rate of 0.0006%, 0.00087%, and 0.001% respectively-- lower than the national average. (these numbers are calculated assuming that all reported incidents of voter fraud were accurate).
An important note on the above figures: That is calculated from the identified voter fraud as self-reported. If we are to assume that voter fraud typically involves voting in two states, then the studies I cited would not be able to identify all incidences of this.
Based on the research above, there does not appear to be any strong evidence that voter fraud is significantly more or less prevalent in states that vote by mail. There also does not appear to be significant evidence of voter fraud at a statistically significant level throughout the United States.