Inga is the love interst of Frederick Frankenstein in Young Frankenstein.
Inga was hired to be Frederick's lab assistant during his stay in Transylvania. Right away there is sexual tension between them as Inga and Frederick have to ride in a wagon full of hay together and when Frederick helps her down, Inga's breasts come precariously close to his face.
When Frederick discovers hs granfather's secret laboratory, he and Inga work together to reanimate a corpse. The time they spend together brings them increasingly closer until in a moment of despair, Inga offers to do anything to make Frederick happy. Frederick and Inga then sleep together in the lab moments before his fiancée shows up.
By the end of the film, Frederick has called off his previous engagement and married Inga instead.
Elizabeth was Frederick's American fiancée. When Elizabeth and Inga meet, there is some tension between the two as Elizabeth is suspicious that Frederick's assistant would be an attractive young woman and Inga had just slept with him. Any underlying rivalry they would have had is presumably resolved as both Elizabeth and Frederick have since moved on.