Oduwa, 19, and Ball, 20, represent manager Mark Warburton's eighth and ninth signings of the summer window.
Both Players are a product of the Tottenham youth system.
Ball spent the second half of last season on loan at Cambridge United, making 11 appearances, whilst Oduwa also appeared 11 times for Luton town.
Ball has represented England at Under-19 and Under-20 level, having previously represented Northern Ireland at younger age groups.
Oduwa has also played for England at youth level, representing his country at the Under-18 level.
Warburton will have both players available this Sunday as Rangers continue their Championship campaign away to Alloa.

Since then the country has seen the creation of a multi-party parliamentary system, a decade-long Maoist insurgency and the abolition of its monarchy.
Flanked by China and India, it is home to eight of the world's highest mountains including Mount Everest, known locally as Sagarmatha.
As one of the world's poorest countries, Nepal's economy relies heavily on aid and tourism.
A devastating earthquake in April 2015 killed thousands of people, flattened villages and reduced numerous heritage sites to ruin.
Since then political infighting has delayed much of the reconstruction despite billions of dollars having been pledged.
Population 31 million
Area 147,181 sq km (56,827 sq miles)
Major languages Nepali
Major religions Hinduism, Buddhism
Life expectancy 68 years (men), 70 years (women)
Currency Nepalese rupee
President: Bidhya Devi Bhandari
Bidhya Devi Bhandari was elected as Nepal's first woman president in a parliamentary vote in October 2015. She is the deputy leader of the ruling Communist Party of Nepal Unified Marxist-Leninist (CPN-UML) and a former defence minister.
She is a campaigner for women's rights and widow of late communist leader Madan Kumar Bhandari.
The post of president is mainly ceremonial.
Prime minister: Pushpa Kamal Dahal aka Prachanda
Pushpa Kamal Dahal was elected as prime minister for the second time in August 2016.
Better known as Prachanda (Nepali for "fierce one"), he led a decade-long insurgency against the monarchy which culminated in the king relinquishing his absolute powers and being forced to give up his throne in June 2008.
He became the first elected prime minister of Nepal in August 2008 but his government collapsed nine months later in a row over his attempt to dismiss the army chief.
Mr Dahal is the leader of the Communist Party of Nepal (Maoist-Centre).
Media freedom is restricted by the fact that journalists have been the victims of violence, activists say.
There is a small film industry, nicknamed "Kollywood".
Some key dates in Nepal's history:
1768 - Gurkha ruler Prithvi Narayan Shah conquers Kathmandu and lays foundations for unified kingdom.
1814-16 - Anglo-Nepalese War; culminates in treaty which establishes Nepal's current boundaries.
1846 - Nepal falls under sway of hereditary chief ministers known as Ranas, who dominate the monarchy and cut country off from outside world.
1950 - Anti-Rana forces based in India form alliance with monarch.
1951 - End of Rana rule. Sovereignty of crown restored and anti-Rana rebels in Nepalese Congress Party form government.
1960 - King Mahendra seizes control and suspends parliament, constitution and party politics.
1991 - Nepali Congress Party wins first democratic elections.
1995-2006 - Maoist revolt which kills thousands.
2008 - Nepal becomes a republic after abolition of monarchy.
2015 September - New constitution adopted - the first in Asia to specifically protect gay rights.
Rangers have signed winger Nathan Oduwa and defensive-midfielder Dominic Ball on a season-long loan from Tottenham Hotspur.
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With its ancient culture and the Himalayas as a backdrop, landlocked Nepal was closed to the outside world until the 1950s.