Strauß began his career at SC Golling. In February 2014, he moved to the youth teams of SV Grödig. Ahead of the 2014–15 season, he joined the renowned academy of Red Bull Salzburg, where he progressed through all age groups in the academy. Before the 2019–20 season, he moved to Germany to join the U19 team of Viktoria Köln.[2] For the Cologne-based club he made 19 appearances in the Under 19 Bundesliga as team captain.[1]
Blau-Weiß Linz
Prior to the 2020–21 season, Strauß returned to Austria to join second division club Blau-Weiß Linz on a contract until June 2022.[3] He made his 2. Liga debut on 11 September 2020, when he came off the bench for Bernhard Janeczek in the 82nd minute on the first matchday of that season against Austria Klagenfurt.[4] By the end of the season, he had made 28 appearances in the second division, scoring two goals.[1]
His performances earned him a call-up to the Austria under-21 team in March 2022, as Altach were involved in a relegation battle.[8][7] Strauß scored his first goal for the club on 2 April 2022, securing a 2–2 draw and a completed comeback against Admira Wacker Mödling deep into injury time.[9] On 20 May, Strauß scored his second goal for the club which would prove to be crucial as his team managed a 2–1 win over WSG Tirol. Thereby, Altach avoided relegation by finishing one point ahead of Admira Wacker Mödling.[10][7] In May, Strauß was named as the winner of Rheindorf Altach's Player of the Season award, given to the club's best player from the previous season.[11]
2022–23 season
Strauß missed the first two league games of the 2022–23 season with an infection,[12] and made his first season appearance for Altach on 7 August 2022 in a league game against Austria Wien. He replaced Lukas Gugganig in the 60th minute, before being forced off due to an injury; it was later confirmed how he would be sidelined for several months as he had "torn his ankle ligament".[13] He was set to return to action on 2 October for the league match against SV Ried,[14] and found himself in the starting lineup from then on under new head coach Miroslav Klose.[15]
Strauß was mainly a starter during the latter part of the season, as Altach managed to stay in the league after being embroiled in relegation battle. He finished the season with 22 total appearances, in which he scored once.[16][1]
2023–24 season
After having been ruled out due to injury at the start of the new season, Strauß established himself as a starter early under new head coach Joachim Standfest.[17][18] He later lost his starting spot and did not regain it. He concluded the season with 10 league appearances—nine of which were in the autumn—and departed when his contract expired in June 2024.[19][20]
Lahti
On 26 July 2024, Strauss signed with Lahti in Finnish Veikkausliiga.[21] Strauss scored his first league goal on 19 September, in a 2–1 home win against IFK Mariehamn. He left the club at the end of the season after the relegation.