It is not unusual to feel all of the above, however, if you intend to portray yourself as a serious and professional candidate you must project an air of confidence and professionalism.
Do not confuse this with arrogance, believe me this is a common mistake. Adopting a cocky manner will only put an interviewers back up and will create such a bad first impression recovery will not be possible.
Interviewers actually expect nerves and apprehension and allow the candidate to settle in taking deliberate steps to help them relax. The absence of nerves may make you complacent which in turn communicates itself to the interviewer. Be grateful for the tense keyed-up feeling, without it you may not perform to your best. The adrenalin tends to push each candidate that little bit more, keeping them on edge and even more determined to convey their message with sincerity and professionalism.
Confidence should be teamed with enthusiasm but beware of falling into the trap and appearing desperate. If you do this, you will lose negotiating power when the actual job offer is made. Remember, confidence is they key but moderately!