Who had an influence on franklin delano roosevelt?

FDR was a classic successful politician, at all times balancing ideology with practicality within the context of maintaining power in a democratic society. In this regard his influence was clearly Macchiavelli (notorious for The Prince, a work which is best understood within the greater context of the rarely read wider Macchiavellian canon), but so is every other politician's. Economically his influence is clearest, he acted in accordance with the economies of John Maynard Keynes, and in doing so helped to alleviate the depression. In terms of ideology he's a tricky one to pin down, but certainly he was classically liberal, Lloyd George having been an obvious influence, as was Marx to a large extent, though not necessarily economically (though Keynes drew much upon Marx). Theodore Roosevelt, Neville Chamberlain and Marriner Eccles may also be regarded as an influences. 
Largely however, he was a pragmatist, he believed in Civil Rights, but was not prepared to isolate the support of Southern Democrats in order to bring it about, hense the "New Deal", he also interned Japanese Americans after Pearl Harbour, a decision that was largely his own but which seems to have troubled him somewhat. 
In all, he was very mush a man of his own mind, whose ideology did much to define progressive liberalism in his time, one may study liberalism, socialism and democracy as ideologies, going back as far as Ancient Greece. He picked and chose his ideology from a number of them. Though to name his top three, Keynes, Marx and Macchiavelli.