The Standard Oil Trust was most likely pictured as an octopus with many tentacles in the cartoon because it showed that this company had influence over several different parts of society.
For example, it shows that one of the tentacles has control of Congress. Congress is part of the legislative branch, meaning they make national laws. This control of Congress shows that Standard Oil Trust is controlling what laws are made in the United States. The octopus is also shown as controlling the White House and other important individuals in Washington DC.