Born in Hundested, Nordstrand played for the local club from he was 5 to 17 years old. He was known for scoring a lot of goals, and his father thought he should move to Frederikshavn and stay at Nordjyllands Sportscollege and play for the local club Frederikshavn fI. After the college stay he moved back to Hundested.
Nordstrand's coach from college contacted Lyngby BK about Nordstrand and his talent, and afterwards he started as senior player in Lyngby. When the club went bankrupt in the winter 2001, Nordstrand moved up from the youth team as one of several amateur players comprising Lyngby BK's first team squad. He made his senior debut in December 2001, 17 years old. He played three league games, as Lyngby finished last in the 2001–02 Superliga season, and underwent forced relegation to the fourth level of Danish football, the Denmark Series.
Nordstrand stayed at the club, and proved himself a goalscorer in the lower leagues of Danish football. Lyngby won promotion to the Danish 2nd Division at the end of the 2003–04 season. Nordstrand formed a dangerous striker partnership with Christian Holst, the pair scoring 43 goals in the 2004–05 season. Nordstrand was the club topscorer with 22 goals, as Lyngby finished third in the 2nd Division that year, and won promotion to the Danish 1st Division.
When Superliga club FC Nordsjælland sold top-scoring striker, and later Danish international, Mads Junker in January 2006, it was initially speculated that Nordstrand would fill his place in the squad. Nordstrand finished the season with Lyngby, and topped the 1st Division goalscorer list with 29 goals, when Lyngby barely missed promotion during the 2005–06 season. Nordstrand decided he wanted top-flight football, and was chased by a number of Superliga clubs, as well as Dutch club FC Groningen. With his Lyngby contract running out in July 2006, he eventually signed a contract with FC Nordsjælland.
In his first season back in the top-flight Danish Superliga, he was the top goalscorer after the first half of the 2006–07 Superliga, with 10 goals in 18 games. Nordstrand was called up for the league national team, which played a number of unofficial national team games in the United States, El Salvador and Honduras in January 2007, by national team manager Morten Olsen. He played in all three games and scored one goal on the tour. On the date of arrival in Copenhagen from the tour, he was selected to the Danish national team for a friendly match against Australia in February 2007. He made his national team debut, when he came on as a substitute in the 86th minute of the match. He has played all matches of this season (33) scoring 18 or 19 goals. Some media says that he has scored 18 goals others say 19, a goal against FCM was scored by either Nordstrand or Lundberg. Which is still discussed.
On 6 July 2007 he moved to F.C. Copenhagen, signing a five-year-long contract with the Danish champions. The transfer fee was reported to be around 15 million Danish kroner (2 million Euro), at that time the largest transfer fee ever paid for a player between two Danish clubs.
In F.C. Copenhagen Nordstrand quickly became an important player. In Danish Superliga season 2007–08 he scored 9 goals and alongside Marcus Allbäck was the team's main attacking force. In the beginning of 2008–09 season he usually started the matches, but he often found himself on the bench with Ailton Almeida and Cesar Santin playing in attack. Despite that, he scored 20 goals in competitive matches for F.C. Copenhagen in the 2008–09 season and was the team's top scorer.
He is also known as Denmarks version of Ole Gunnar Solskjær because of an old nickname "Babyface Assassin".
In August 2009 Nordstrand signed for Dutch Eredivisie club FC Groningen on loan, as a replacement for fan favourite and fellow Scandinavian Marcus Berg. In his debut game with his new club, he provided the only goal in a derby against SC Heerenveen, ended in a 1–0 win for FC Groningen, the first in the Eredivisie season for the Green-Whites. On 23 March 2010 FC Groningen announced that Nordstrand returns to the new season from Ehrendivisionär to the Danish double winners F.C. Copenhagen. Groningen will not consider the purchase option of the 26-year-old striker.
On 17 January 2012 Nordstrand signed a contract with FC Nordsjælland effective 1 July same year.
On 14 December 2014 Nordstrand signed 1-year contract with AGF. He left the club on 1 January 2016.
On 28 January 2016 Nordstrand joined Australian club Newcastle Jets. Following a positive performance including 4 goals in 11 appearances, Nordstrand signed a year extension of his contract.
On 3 June 2017, Nordstrand signed with Danish 1st Division-side Fremad Amager.Scores and results list Denmark's goal tally first.
Danish Superliga: 2008–09
Danish Cup: 2008–09, 2011–12
Danish Superliga topscorer : 2008–09