The given sentence is a type 1 conditional sentence. It shows a possible condition and its probable result. Here, the verb tense of the conditional clause is in simple present and the verb tense of the main clause is in simple future tense.  
The context refers to the condition of (unless) him being offered more money elsewhere and if that that condition is not fulfilled, then he (will) accept this job. 
Option C uses the contraction of the simple future tense verb (he will) "he'll accept". This concurs with the context. Thus, this is correct.
"He won't accept" is a negative clause and does not follow the conditional. Thus, this is incorrect.
"He would accept" is incorrect as it indicates a preference or a wish. However, the context requires a simple future tense statement.
"He wouldn't accept" is also a negative clause and does not concur with the conditional 'unless" in the context. 
Thus, option C is the correct.