I
verb
BAD : I don't think that longer prison sentences would influence on criminals.
GOOD : I don't think that longer prison sentences would influence criminals.
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influence sb/sth (WITHOUT on ): 'The revolution of 1789 influenced events far beyond France.'
Note the alternative: 'I don't think that longer prison sentences would deter criminals.'
II
noun
1
BAD : These drugs have no influence on the virus.
GOOD : These drugs have no effect on the virus.
BAD : I asked him not to keep disturbing me, but it had no influence.
GOOD : I asked him not to keep disturbing me, but it had no effect.
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If someone (or something) has an influence , they help to shape the way that someone or something develops: 'D.W. Griffith had an enormous influence on the motion picture industry.'
If something has an effect , it causes a change to take place in someone or something: 'The war had a disastrous effect on the economy.'
2
BAD : America has given a tremendous influence to Japanese society.
GOOD : America has had a tremendous influence on Japanese society.
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have an influence on sb/sth (NOT give ... to/in/for ): 'The book attempts to demonstrate the influence of the stars on people's lives.'