I'll cut to the chase.
NZ
Once upon a time - we used to have a dominant record against NZ and they were our bunny. Now lets look at our ODI record against them in recent teams in bilaterals.
2015/16 -> 2-0 to NZ in NZ (this was the series Babar and Hafeez scored big for us but NZ were just better)
2014/15 -> 2-0 to NZ in NZ (this was a short ODI tour of NZ arranged right before the WC and they amassed 370 against us in the 2nd game)
2014/15 -> 3-2 to NZ in UAE (this series marked Haris sohail return to the ODI side but we just could not chase 250-300 scores against them atleast we scored 363 against them in Sharjah thanks to Shehzad)
In fact, the last time we beat them in a bilateral ODI series was in 2010/11 when we beat them 3-2 and saw a young Shehzad blaze away at the top of the order.
Pretty poor record against an ODI side that is not considered one of the best.
SAF
Now lets look at our bilateral ODI record against SAF - now I know the last time we played them in bilaterals in 2013, we beat them 2-1 in SAF and saw Shehzad score a fantastic ODI hundred there but lets look at our record prior to that.
2013 -> 4-1 to SAF in UAE (SAF toured us and resoundingly beat us in almost every game including one game where we lost our last 6 wickets for 20 runs and failed to chase 184

)
2012/13 -> 3-2 to SAF in SAF (we toured SAF earlier that year and lost 3-2 to them)
2010/11 -> 3-2 to SAF in UAE (this series is perhaps most fondly remembered for Razzaq's ATG knock of 108 to chase 290 odd in the 2nd ODI. Sadly it was the only highlight of a tough series that saw Zulqarnain Haider run away and seek asylum

)
2007/08 -> 3-2 to SAF in Pakistan (this series was one of the last time a top team toured Pakistan - an almighty collapse in the 5th ODI chasing only 230 odd led us to lose this series as well...)
England
This is truly horrendous since England were not even a decent ODI side until recently and were amongst the worst yet we still outdid them in losing to them for so many years...
2016 -> 4-1 to England in England (less said the better - England scored a world record 444 against us in the 3rd ODi and we were thrashed like no end. Winning the final game by chasing 300+ was of little consolation to us
2015/16 -> 3-1 to England in UAE (we looked good in the first game when Hafeez scored his last ODI hundred to date and easily chased down a below par total by England but it all went downhill from there fast. Had to chase 356 in the series decider and just got blown away....)
2011/12 -> 4-0 to England in UAE (we were led by Mohsin "I beat England 3-0" Khan and got blown away in the ODI series after winning the Test series. Our batting was simply not up to par...)
2010 -> 3-2 to England in England (right after the Spot Fixing Scandal so our morale was very low at the time. Umar Gul bowled amazingly well and was our only highlight of this series as we lost the series decider to lose 3-2 after coming back from 2-0 down)
2006 -> 3-2 to England in England (this series saw YK score his first ODI hundred against a top team. That was probably the only highlight of this ODI series as again we went down 3-2 losing the series decider)
In fact, the last time we beat England in an ODI series was back in 2005 when we beat them 3-2 when England toured Pakistan! That was 12 years ago!!
Australia
This now is truly horrific and possible our worst cricket record right now - let me begin.
2016/17 -> 4-1 to Australia in Australia (Tbh, I had little expectation and was overjoyed when we leveled the series 1-1 and kept Warner and Smith at bay up until that point. Things went quickly downhill and we had to chase 350+ in our last two games and got blown away like a feather in a hurricane...)
2014/15 -> 3-0 to Australia in UAE (this series came right after the high of winning 2-0 against Aus in tests - ODI's was a completely different story as another collapse led to a 3-0 defeat at home. This also saw Fawad Alam's poor ODi run and saw him dropped for the WC squad.)
2012 -> 2-1 to Australia in UAE (we actually did okayish in this series that also saw Nasir Jamshed hit form right before the Aane Do series but again were not quite good enough as we lost this series too.)
2009/10 -> 5-0 to Australia in Australia (this hurts the most - never saw us lose 5-0 up until that point but the 2009/10 period was truly painful and demoralizing for Pakistan cricket. Just not up to par as they memories of that Sydney Test was still fresh in our minds. Blown away again.....)
2009 -> 3-2 to Australia in UAE (ANOTHER defeat to Australia

we were so poor in this series as we were struggling to score even 200 on the UAE pitches. Did well in the final game was we chased 254 for the loss of only 3 wickets thanks to a Kammy century but was too little too late)
2004/05 VB Series -> 4-1 to Australia in Australia (technically this was a tri series involving WI but i will mention our games against Aus only - lost every single game against them barring one

The only highlight was Salman Butt's form but this was another miserable tour....)
In fact, the last time we beat Australia in an ODI series was in 2002 in Australia when we won 2-1. That was 15 years ago!!!
Seems like we can only beat SL, India, WI, Bangladesh and Zimbabwe in bilateral ODi's
It pained me to even write about this but I hope with Mickey Arthur - we can beat them good teams consistently in bilateral ODI series.
Comment away folks! Don't be shy.