In comparing Oliver Twist to Jane Eyre, it might be a good idea to list their common themes and then explore those themes in greater depth.
Life is hard for orphans. Both Oliver and Jane are orphans and have to grow up in a harsh, unforgiving environment. They live at a time when there was no little or no government help or support for the poorest members of society, including children. And so they're pretty much at the mercy of adult authority figures, who proceed to treat them abominably. Which leads us on to our next theme.
Adults can be so cruel. Poor little Jane is treated abominably by Mrs. Reed and her vile progeny. Deprived of love and care, Jane is forced to live a cold, lonely existence in Gateshead. Things don't get much better when she heads off to Lowood School, where she's also singled out for mistreatment.
Oliver is born and raised in a workhouse, a horrible place where he's overworked and never given enough to eat. Adult authority figures like Mr. Bumble treat him with contempt, and even when Oliver finally leaves the workhouse, he continues to be exploited. As well as the disgraceful treatment meted out to him by Noah Claypole, Oliver has to endure being used by criminals like Fagin and Bill Sikes to steal other people's property. As a result, Oliver is shot and almost killed in a burglary in which he's forced to participate by the unspeakable Sikes.
There's always hope. Despite their many adversities, both Oliver and Jane experience a happy ending. Jane marries the man she loves, Mr. Rochester, and Oliver ends up in the loving bosom of his late mother's family. The message in both cases seems to be that the prospect of entering into a strong, loving family provides hope for those who've had to endure such miserable childhoods as Oliver and Jane.