Based on the Euler beam theory and a Galerkin formulation using natural modes, the nonlinear vibration behavior and stability of electrostatic driving fluid-conveying micro (straight or curved) beams are studied in the paper. The focus of this study is on the critical coupling of fluidic, mechanical and electrostatic effects in the nonlinear system. Under these effects, micro devices may exhibit (dynamic) snap-through or/and pull-in instabilities. Our study reveals, for the first time, the effects of the velocity of the inner fluid on the bifurcation diagrams for complex nonlinear systems. It is also found that fluid can be utilized to efficiently tune the frequency of straight beams over a wide range. For curved beams, the tuning can be achieved easily by adjusting the voltage. These findings are beneficial in many applications of the electrostatic microelectronic mechanical systems (MEMS). In addition, phase plane analyses are performed in this study, and more complicated phase portraits for different initial conditions are obtained as well. It is found that the homoclinic connections on the phase plane are directly related to the dynamic snap-through or dynamic pull-in instabilities; and the periodic orbits are directly related to the periodic motions of micro beams. These findings can provide reasonable explanations for the experimentally-observed phenomena for micro sensors, and are beneficial to the optimization design of MEMS.