With apologies for using Wikipedia here.
One of the Nazi members, Baron Wolfgang von Strucker, quickly seized control of the Hydra organization and restructured it to be dedicated to world domination through terrorist and subversive activities on various fronts, resulting in a global neo-fascist New Order. To this end, Baron von Strucker used his personal fortune, based on his recovered hoard of Nazi plunder from World War II, and funds established by the original leaders of the Japanese secret society that became part of the old Hydra.
However, after von Strucker's first death, Hydra broke into factions (such as A.I.M., Secret Empire, Them, etc.) that each adopted its own reorganized modus operandi. Eventually, this fragmentation would lead to a Hydra civil war, even after von Strucker's resurrection.
According to the files discovered by Nick Fury, Hydra is split into four independent sectors:
International Corporations (Fronts created using a legitimate business to conceal illicit activities)
Government Assets (Individuals within the chain of command. Long-term resources that benefit from the minimal turnover inherent in bureaucracies)
Global Criminal Groups (Subsidiary organizations created for short-term goals. Also used to deflect unwanted interest from the global law enforcement community)
- Intelligence Gathering (S.H.I.E.L.D. and all their underlying resources) Hydra regards S.H.I.E.L.D. as their "most valuable proactive intelligence asset" while its government assets include the US Department of Treasury, the FBI, and the NSA as well as the Canadian Security Intelligence Service and the GRU and SVR of Russia.
So, a mixture of old and new money from von Strucker and the corporations that his organisation created to front research and profit...
Where Stark's fortune is based on intellect and ego, Hydra's technological advances are facilitated by alien tech.
Hydra's level of technology is as highly advanced as that of any on Earth, based in part on technology of the alien Gnobians discovered by Baron von Strucker in 1944
It seems fair to assume that some of this technology is sold to consumers/governments/etc., resulting in both profit and infiltration opportunities.