It's doubtful you score will increase immediately, because your just playing 3-Card Monte with your debt by taking out the loan.
Also, your APRs are way too high. Get those reduced, if you haven't missed a payment in over six months, it's quite easy to get an APR reduction. Even with poor credit (I have a TU 547, EQ 516) and I was able to get AMEX to reduce my Delta card from 29.99% to 18%. And my orchard and firt premiere, which had been at the penalty APR of 29.99%, dropped down to 9.99% with 3 consecutive months of paying.
The reason why I say this is, with APRs in the mid to high 20s, your debt doubles in about 2.5 years. By reducing the APR, you'll have a lower minimum payment, which means that the more money you throw at the debt, the more is used to decrease principle, not interest.
Your overall indebtedness isn't going to change by getting a loan, just how you owe and at what interest rate. Decreasing your CC balances, however, will boost your score.