Can I cash a check made to the irrevocable trust as a trustee and benif. of said trust

Yes, as long as the trust terms provide for the method of distribution. It is your job as trustee to manage the finances of the trust. What makes you think you wouldn't be able to cash checks? Maybe I'm missing something from your question.

The best business practice is to deposit the checks into the trust's bank account. Then write checks to distribute the proceeds. This leaves a nice clean paper trail of where the money goes. Cashing checks breaks the clean paper trail. You then need to create payment transmittals and signed receipts from each recipient to achieve a similar level of confidence. In as much as the Trustee bears a fiduciary responsibility to the beneficiaries the quality of your accounting should be above reproach.

As the trustee for the trust, you should be depositing checks into the trust account, then issuing disbursements according to the terms of th trust.