Can I reapply immediately?
Yes, though whether wise to do so may in part depend on the exact wording of your refusal letter. However given I got admission to an Oxford summer course (ie time is of the essence) and what you state of the refusal reasons (ie basically the issues were documentary) I think you have little choice but to do so.
And yes, at the very least any further application should address the stated issues:
I] explain any apparent discrepancies between bank statements and personal income for your father, and
2] state your father's employment status.
You may also wish to consult a reputable agent (such as an immigration specialist who is a member of the UK Law Society) who should at least be able to ensure that the paperwork for any further application is in order prior to submission.
Please also note that for any more specific question about UK study visas Expatriates may be a better place to ask than here.
General guidance from GOV.UK.