Can I fly IFR in VMC if my instrument rating is not current? If my IFR rating is not current, does this mean I can't fly by IFR, or does it just mean that I can't fly in IMC?

It seems that if it's just the latter, then it would make sense to fly IFR if the weather is still VMC. It would allow me to stay current on procedures while waiting for the opportunity to get my rating current.
No, you cannot. 14 CFR 61.57 (c):


  (c) Instrument experience. Except as provided in paragraph (e) of this section, a person may act as pilot in command under IFR or weather conditions less than the minimums prescribed for VFR only if: [instrument currency requirements]


To accept an IFR clearance as PIC, even in VMC, you must be instrument current.