when I am accelerating/shifting my car just dies but theres still power.how/why

the oil level is not always correct due to a slight oil gasket leak but its about a quart low and I usually shift at 3500 or 4000 so I would assume it drops to 2000-2500 rpms by the time I get it to the next gear. my o2 sensor is out but that's because have a Frankenstein build 2.3L block with2.2L head that has vtec and they both run at different temps....soo I was told. i do however have the receipt to the engine build, which just Probably made the question a little bit harder.

Doesn't make it any harder for me! I'm not the one actually doing the work!....Anyhow , just to clarify , before going to much further , It primarily cuts-out (stalls) on you BETWEEN 4th and 5th , or does it lose POWER as you go into 5th gear? Is the check engine light on? Next in the series of questions to clarify...Did this engine come in the car when you bought it , or did you put the engine in? How long have you had it? Are ALL engine harness grounds clean and tight? Has distributor been visually inspected internally for shaft movement or oil leaking into it? PCM is for the V-TEC head & all sensors match the PCM?