They somehow lost the Queen family fortune, including all personal assets like Moira's jewellery, cars, etc (which they otherwise should have kept and been able to sell).
Then Thea inherited Malcolm Merlyn's millions / billions, but I'm not sure what happened to all that money. It's not clear whether Thea doesn't like using it because it's Malcolm's money and therefore only uses it in "emergencies" or whether Malcolm somehow stole it from Thea (although as head of the LOA, he would presumably have access to plenty of funds or the means to obtain funds if needed).
As others have said, whether or not Oliver personally has money or access to lots of money just depends upon the needs of the script from week to week. It's a problem across all of the CW shows. On The Flash, Wells left his fortune to Barry, yet Barry was living at home and then with Cisco instead of living in Wells' mansion or his own apartment. Similarly, Cisco and Caitlin apparently still get paid by Barry, but Barry won't rebuild STAR Labs. And Supergirl has a HUGE apartment, despite earning what would be a relatively low wage as a trainee journalist (unless Cat Grant paid her really well and she purchased her apartment).