As trillions of dollars flow out the door, stimulus oversight is showing signs of strain.

Lawmakers have unleashed more than $5 trillion in relief aid over the past year to help businesses and individuals through the pandemic downturn. But the scale of that effort is placing serious strain on a patchwork oversight network created to ferret out waste and fraud.

The Biden administration has taken steps to improve accountability and oversight safeguards spurned by the Trump administration, including more detailed and frequent reporting requirements for those receiving funds. But policing the money has been complicated by long-running turf battles; the lack of a centralized, fully functional system to track how funds are being spent; and the speed with which the government has tried to disburse aid.

The scope of oversight is vast, with the Biden administration policing the tail end of the relief money disbursed by the Trump administration last year in addition to the $1.9 trillion rescue package that Democrats approved in March. Much of that money is beginning to flow out the door, including $21.6 billion in rental assistance funds, $350 billion to state and local governments, $29 billion for restaurants and a $16 billion grant fund for live-event businesses like theaters and music clubs.

The funds are supposed to be tracked by a hodgepodge of overseers, including congressional panels, inspectors general and the White House budget office. But the system has been plagued by disagreements and disarray.

President Biden has tapped a longtime economic adviser, Gene Sperling, as his pandemic relief czar. Mr. Sperling has been racing to stand up the oversight architecture and is relying heavily on the investigative powers of the Pandemic Response Accountability Committee, a panel of inspectors general, in addition to the Government Accountability Office and the administration’s Office of Management and Budget.

“When you have a rescue plan, there is going to be a certain amount of tension between aspiring for perfection and meeting the law’s fundamental aims to move funds out in time to cut child poverty, keep people in their homes, save small businesses, restaurants and child care centers,” Mr. Sperling said in an interview. “You just have to do everything in your power to strike a rigorous and right balance.”

So far, major instances of fraud and waste represent a relatively small percentage of the 2020 initiatives and have been largely confined to small business lending efforts, like the Paycheck Protection Program and Economic Injury Disaster Loans. But federal oversight experts and watchdog groups say the exact scale of problems in the $2 trillion bipartisan stimulus relief bill in March 2020 is virtually impossible to determine because of insufficient oversight and accountability reporting.