In this sentence:
His support gave me strength and inspiration to continue my campaign without wavering.
does using the before strength imply a restriction?
His support gave me the strength and inspiration to continue my campaign without wavering.
Is there any difference in meaning between the two?
Both are correct and near identical in meaning.
If I really had to pin it down, I would say the latter wording of 'the strength' implies he was the sole source of your strength and inspiration for your campaign, whereas the former is more general and perhaps only implies his support contributed some amount to your courage.
If you refer to the strength, your use of the definite article gives the feeling that you are referring to a unique strength, in this case that needed to continue the campaign. Such support might be financial, political or other. If you omit the you give the feeling of a more general statement that he reinforced your general strength of character or confirmed your opinion that you were doing the right thing.
His (financial) support gave me the (financial) strength ...
His (generally encouraging) support gave me (emotional) strength ...
Like some of the other answers, I agree that the meaning is practically the same. Usage of the definite article adds a degree of portentousness to your statement. It is useful for adding emphasis and conveying a note of criticality.
One thing worth mentioning is that use of "the" in cases like this is often followed by an indication of need. For example: "... Gave me the strength I needed". This explicitly states that the unit of strength given was necessary and not simply supplementary. One could argue in cases where the explicit statement of necessity is omitted, that it is still implicit; however, I know English is too fluid for that to be universally true. Still, as a general rule of thumb, if adding something like "I needed" after the statement doesn't change the intended meaning, then I usually use "the", otherwise I do not.
