The DOT can raise revenue by road tolls
See USA Today
The 1956 Interstate Highway Act generally bans tolling on interstates.
The Department of Transportation cannot add tolls on its own. It would need congressional authorization.
Medicare/ss can garnish small amounts of wages that aren't worth fighting in court
There is a thing called a class action suit, where small amounts can be aggregated into large amounts so as to make them "worth fighting in court". Medicare and Social Security combine for a 15.3% tax on income and almost half of federal government spending. They are the two largest federal programs with Defense a distant third. Any amount small enough to not be worth fighting on an individual basis isn't going to make much of a difference in their budgets either.
DOA has tariffs
Department of Agriculture? It does not have tariffs, and the agency that does can't change them on its own.
HUD has rents
Mostly Housing and Urban Development subsidizes housing built and operated by states and localities. I believe that you will find that HUD has very few properties of its own on which it can charge rent.
Dept. ed has loans
Sure, the Department of Education has loans, but they are constrained by law to operate a certain way, and that way is not profitable.
military has arms sales
Mostly military suppliers have arms sales. The military itself generally sells surplus at a loss rather than new arms at a profit.
science and foreign affairs are basically military
While there is considerable military-funded research, there is also government civilian-funded research. And the Department of State would be quite surprised to find that they are part of the military. And the military would be surprised too; doubtless they will want to make a lot of changes when they discover that. There may be a sense in which that is true, but that sense is not budgetary.
Is there any situation where the Congress or president would have any control over government spending?
Well, considering that the president appoints the people who run all these departments and can give them orders, any flexibility that they do have is under presidential control. So yes, the president certainly has some influence.
Beyond that, Congress sets the laws under which the departments operate, including their budgets. Further, none of these departments is self-funded. They all need subsidized by the general funds (except possibly Transportation and Treasury).