I am sorry to learn of your poor experience with the home inspectors.
In general you can sue a home inspector for negligence and breach of contract if their conduct falls below the standard of care for their profession, or if they fail to perform the inspections that they agreed to do in their contract with you (most claims include both causes of action).
Unfortunately, the FHA inspection focuses on protecting your FHA lender (not you, the buyer), so these inspections can be rather cursory. However, even a cursory inspection must still be truthful and accurate. If the inspection report misrepresents or misstates the factual conditions of the property, you have a cause of action against the inspector.
With regard to the pest inspector, that is easier as you have a direct claim against them (you hired them (through your agent) and they simply failed to do their job properly).
Short of filing a lawsuit, you can try to mediate the dispute with them - contact your local bar association and request referrals to mediators, a third party neutral can often help you reach a mutually agreeable resolution. Use the bar association's referrals to contact a mediator or two, the mediator will then contact the other party to set up a mediation session, and you can go from there - hopefully resulting in a formal or written settlement agreement, and save yourself the time and expense of litigation.