Sheffield-born Oliver has spent the last two seasons at Gillingham, netting 27 league goals in 77 starts after arriving from Northampton Town, where he helped the Cobblers to promotion from League Two in 2019-20.
Oliver, who started his career with Sheffield Wednesday's academy, has previously played for Lincoln City, Crewe Alexandra, Morecambe and York City, in addition to loan stints at Notts County and Mansfield Town.
Halliday, the Redcar-born player, heads to Valley Parade following the cancellation of his contract at Fleetwood Town by mutual consent.
Halliday, who started his career with Middlesbrough academy and has also spent a previous spell in Yorkshire at York City on loan, was City's 12th signing of the close season with Oliver the 13th arrival of the summer.
On Friday, Doncaster announced their latest signing in the form of former Harrogate Town striker Josh Andrews while the Sulphurites' latest arrival was the loan signing of Wolves defender Lewis Richards.
More signings could be on the way and there are a number of free agents available to Yorkshire's League Two clubs and we have picked the best 17 players - based on their Transfermarkt market value - without a club who have been released by fourth-tier clubs.
1. Luke Murphy
The ex-Leeds United midfielder was released by Crewe Alexandra after two seasons in his second spell with the club. Market value: £540k. Photo: Getty Images
2. John Bostock
The player is a free agent after turning down a new contract offer from Doncaster Rovers. He joined Rovers on an 18-month deal in January 2021. Market value: £450k. Photo: Getty Images
3. Callum McManaman
The winger made 29 appearances and scored two goals before being released by Tranmere Rovers after one season at the club. Market value: £450k. Photo: Getty Images
4. George Williams
The 26-year-old spent one season at Barrow before being released by the club. Market value: £360k. Photo: Getty Images