Recurrent issue during cruise, Altitude Alert

Greetings ladies and gents !!

Hopefully you guys can shed some light on this issue. Few minutes after reaching cruising altitude and leveling off without any problems my bird goes crazy. It seems to ignore LNAV and VNAV because it starts to climb out of the selected flight level at which point I get the Altitude Alert EICAS message and it also deviates from its lateral path. I have done all my weight and balance and fuel calculations correctly, also turbulence effects are disabled. I don't know if its because of REX or the wind speeds aloft and its direction. I have noticed as well that usually it does not complies with the selected MACH speed for cruise(it usually stays at MACH .80 when it should be .83 or .84 as shown on the FMC) at this point if I try to intervene with A/P engaged with HDG select to get back on track, and it banks sharply over 30 degrees and stalls(BANK angle selector is in AUTO) or if I try to correct the altitude it's either no response or it climbs or descents abruptly. Any suggestions...ideas or tips greatly appreciated.!!

Thanks