Oram suffered a hamstring strain before the second Test against South Africa and Vettori said he was hopeful the 29-year-old would finally be fit for the first one-day international in Durban on Sunday.
''The one-day internationals are the most important games ahead, so hopefully Jacob will be able to play in those,'' Vettori told reporters.
Martin is still feeling the effects of the stomach virus that laid him low in the latter stages of the second test.
New Zealand lost the two test matches by 358 runs and an innings and 59 runs and Vettori believes the twenty20 and three ODI games that follow are an opportunity to restore pride.
''It's a chance for us to redeem ourselves,'' he said. ''We've taken solace in the fact that we've been pretty good operators in twenty20 and one-day cricket over the last few years.
''The guys know their one-day games pretty well and the fact we had the recent Twenty20 World Cup here, where we made the semis and South Africa did not, and the guys got a good feel for the pitches will be of assistance to us as well,'' Vettori said.
Tomorrow's Twenty20 international is in Johannesburg.