Venno was born in Tartu, and started his career in hometown club Pere Leib Tartu at the age of 16. In addition to three Estonian League silver medals he won the Estonian Cup in 2008 with the and reached the finals of the Baltic League twice. Venno was named the Best Young Estonian Volleyball Player in 2008 and 2009. In summer of 2009 Venno signed with ACH Volley Bled of Slovenia."ÕL: Oliver Venno võtab Sloveenia klubi hea hüppelauana" SPORT.ERR.EE (06.09.2009). Retrieved on 11.06.2012. With the Bled team Venno won the Slovenian League, the Slovenian Cup and the MEVZA Cup. They also reached the Final Four of the 2009–10 CEV Champions League making Venno the first Estonian to play in the semi-finals of the Champions League. In 2010 and 2011 Venno won the Estonian Volleyball Player of the Year award. From 2010 to 2012 he played in Germany for VfB Friedrichshafen and won the German League and the German Cup once. Venno started the 2012–13 season in the Montenegrin top team Budvanska Rivijera Budva."Venno liitub Meistrite liiga klubiga" Sport | ERR (15.09.2012). Retrieved on 15.09.2012. He left the team in December and joined his compatriots Raimo Pajusalu and Keith Pupart in the French team Rennes Volley 35."Oliver Venno liitub Prantsusmaa eestlastega" volley.ee (14.12.2012). Retrieved on 08.01.2013.
