Ouseph, 30, became the first Englishman in 27 years to win the men's singles title with a narrow 21-19 21-19 victory over home favourite Anders Antonsen.
The husband-and-wife Adcocks beat Danes Joachim Fischer Nielsen and Christinna Pedersen in the mixed doubles final.
Scot Kirsty Gilmour lost in the women's singles final to Carolina Martin.
The Spanish top seed triumphed 21-14 21-12.
It is the first time England have won two golds at the Euros since 1988, when Darren Hall won the men's singles and Gillian Clark claimed the mixed doubles title with Danish partner Steen Fladberg.
The success at the Euros comes after GB Badminton had all its funding cut by UK Sport before the 2020 Tokyo Olympics.
Ouseph, who had previously won two bronzes and a silver in the men's singles at the European Championships, is just the third Englishman to win the event with Steve Baddeley the previous player to triumph in 1990.
Between the wins for Baddeley and Ouseph, players from Denmark had won gold in eight out of nine European Championships.
The second-seeded Adcocks took full advantage of their first appearance in a Euros final to see off top seeds Nielsen and Pedersen, who had won the event in the past two Championships.
The Adcocks were pegged back after winning the first set but held their nerve to triumph 21-17 18-21 21-19.

Ivor Miller, 27, who has learning difficulties, was chased by the group after one member called him "a beast".
The 27-year-old sought refuge in a derelict flat and jumped out a second floor window suffering severe injury.
At the High Court in Glasgow, judge Norman Ritchie QC ordered a 17-year-old man to be detained for six months.
The judge told the eight accused: "This whole incident, some of which was captured on CCTV, is extremely disturbing.
"The group, like a pack of animals, turned on an entirely innocent young man for no good reason other than he behaved differently because he has learning difficulties."
Three of those who pursued Mr Miller were originally charged with attempted murder.
Michael Clare, 21, from Airdrie, North Lanarkshire, and two 17-year-old youths, who cannot be named for legal reasons, had their guilty pleas to charges of assault accepted.
All three admitted attacking Mr Miller by chasing him into the common close at 52 Howard Street, Glasgow, on 4 August last year.
All three, and another 17-year-old youth, a 16-year-old girl, a 16-year-old youth and 23-year-old David Newlands, from Maryhill, Glasgow, admitted committing a breach of the peace and placing Mr Miller in a state of fear and alarm.
Newlands also pleaded guilty to punching Mr Miller on the head in the Hootenanny pub in Howard Street.
Jade Park, 19, from Glasgow, who sparked the incident by falsely calling Mr Miller "a beast" admitted punching him in Jamaica Street and in the Crystal Palace pub.
Judge Ritchie sentenced a 17-year-old male to six months detention for assault.
He deferred sentence on Park, who is about to give birth, until June for good behaviour and imposed a community payback order on all the others and ordered then to perform 150 hours unpaid work in the community.
England claimed two gold medals as Rajiv Ouseph and Chris and Gabby Adcock triumphed in finals at the European Badminton Championships in Denmark.
[NEXT_CONCEPT]
Eight people who chased a vulnerable man until he threw himself out of a flat window in Glasgow have been called a "a pack of animals" by a judge.