Oneida is one of Wanganui's most distinguished rural homes. It was built in 1870 for Joseph and Mary Ann Burnett. Joseph had emigrated from England to the United States in 1830 in with his parents and siblings. He met and married his cousin Mary in 1833, and soon after moved to Utica near Trenton, Oneida County, New York State. Following several attempts to settle in both America and England, the couple eventually immigrated to New Zealand in 1856. They settled in Wanganui where Joseph established himself as a confectioner and baker. In 1860 they acquired a 170-hectare property east of the township, but it was another decade before the family were able to move into their new house.

Although the plans for Trenton House (now more commonly known as Oneida) were prepared by George Frederic Allen (1837-1929), a surveyor and architect in the Wanganui region, the design owes much to the architecture that the Burnetts saw during their time in the United States. The steeply pitched roof, lacy barge boards, windows with pointed arches, one storey porch and asymmetrical plan were all common to the Carpenter Gothic style which developed in America during the 1830s and 1840s. Constructed from heart totara and kauri, the house was completed in 1870. An unusual feature for its time was the central hall. This rises 13.5 metres from the ground floor to the apex of the roof and is broken halfway by an organ loft and railed gallery. There have been several alterations to the building including the addition of a verandah in 1880. Joseph Burnett died in 1893 and the property passed to his sons Cornelius and Alfred. The property was divided and Cornelius inherited the house. The property was eventually farmed by the third son of Cornelius, Benjamin Ward Burnett. Benjamin lived at Oneida until his death in 1975, and the house was sold the following year to the Bryant family. The latter, with the help of the New Zealand Historic Places Trust, undertook restoration of Oneida.

Oneida is significant as it is one of the finest examples of the Carpenter Gothic style in New Zealand. It is also associated with Joseph and Mary Burnett, early Pakeha setters to the Wanganui region. They and their descendants lived in the house for over 100 years.