See studies by K. Wiekart (tr. 1965) and E. Taverne et al. (2001).
In 1933 Oud became minister of Finances, in the second cabinet led by Colijn. As minister he was responsible for a large scale operation of budget cuts, during a time of economic crisis. In 1935 he proposed the Bezuigingswet 1935 (the Budget Cut law 1935) which involved many budget cuts and financial reorganisations: salaries of civil servants were lowered, the old age pensions were financed in a different way and for budgettary reasons, soldiers were to become civil servants after a certain period. Although his proposals lead to a political crisis, they were nonetheless carried by parliament. In the same year, after Marchant left the VDB after a scandal, Oud succeeded him as political leader of the VDB. Oud led the VDB in the 1937 elections and returned to the Tweede Kamer as chair of the parliamentary party. He also served as chair for the Committee on government expenditure.
Controversially, Oud stayed mayor after German invasion of 1940, although he was not a member of the national-socialist NSB. During his period as mayor, he was heavily involved in the reconstruction of the centre of Rotterdam which heavily destroyed by the German bombings. He was heavily criticized by Dutch politicians for cooperating too much with the NSB, while the NSB criticized him for being uncooperative. In the spring of 1941 he was harassed brutally by members of the NSB, twelve party-members invaded the City Hall, gagged Oud, adorned him with Freemason-like symbols and made pictures of him. In the autumn of 1941 he left his post at his own request, he also stood down as member of the provincial legislative of Rotterdam. He was succeeded by Frederik Ernst Müller. In the summer of 1942 he was briefly held in Sint Michielsgestel, where many prominent Dutch politicians were held capitive. During the war Oud kept far from the resistance movement and instead committed himself to writing several books on parliamentary history. Meanwhile he kept close contact with important people from the business and the political world of Rotterdam.
In 1945, after the liberation of the Netherlands, he returned to Rotterdam as mayor, although he was also asked to become mayor of Amsterdam, and he was officially re-appointed in 1946. In the same year the VDB fused with the social democratic SDAP and the leftwing Christian CDU to from the Labour Party. Oud was one of the co-founders of this party and served on the party's board between 1946 and 1947. Meanwhile he served on many government, business, international and civil society committees, he chaired the government committee for municipal finances between 1946 and 1954, he was member of the board of trustees of the banker Staal, he was member of the pensioncouncil of the Dutch Reformed Church since 1946 and he served as chair of the International Union of Municipalities and Local Governments between 1948 and 1954.
He immediately founded the Committee of Preparation of the Foundation of a Democratic People's Party, which prepared the foundation of the VVD. He negotatiated the merger of the remnants of the old VDB with the newly founded Freedom Party. On January 24, 1948 he became one of the founding members of the liberal VVD, together with Stikker and Korthals and served in its first national board as vice-chair. In 1948 he was elected into the Tweede Kamer for the VVD, and became chair of the VVD-parliamentary party, he combined this position with the position of chair of the party's organisation.
In parliament he mainly spoke on issues of administrative and constitutional law. He was a very influential member of parliament. When the law concerning the decolonisation of Indonesia, a very controversial issue, was voted on the two-thirds majority was only reached because of amendment proposed by Oud, which was taken over by the government, ensured the support of the VVD. In 1950-51 Oud came into conflict with the VVD minister of Foreign Affairs, Stikker over the policy concerning New Guinea. Between 1950 and 1953 he was a member of the Government Committee Van Schaik, which prepared a constitutional change. In 1952 he did not seek to be reappointed as Rotterdam's mayor, and instead became extra-ordinary professor of Constitutional Administrative law at the University of Rotterdam, which he remained until 1957. Between 1953 and 1963 he was chair of the Justice Committee of the Tweede Kamer. As such he was heavily involved in the preparation of many laws, and served as chair on the committees preparing the laws on the provinces, the police, archives, patents and many more. In 1959 he came into conflict with Van Riel, the chair of the VVD's parliamentary party in the Eerste Kamer, because Van Riel wanted to become minister, but Oud denied him this.
In the last years of his period in the Tweede Kamer, Oud was the eldest member of the house and on many times functioned as chair, when a new chair was elected for instance. Before the 1963 elections Oud announced that he would not continue as MP, he was succeeded by the minister of Home Affairs Edzo Toxopeus. In the same year he was appointed as Minister of State, an honorary title.
When Oud died in 1968, his family wanted to announce his death after the burial. His GP did not know this, and told a patient that evening that Oud had died that afternoon. The father of this patient happened to be a journalist for the socialist paper Het Vrije Volk, which published a large In Memoriam the next morning.