I think if your visa is expired, you need to get a new visa if the travel is outside US. That is to my knowledge. You cannot travel on an expired visa.

You can definitely travel with expired USA visa as long as you have other proper documents for the county or place you are visiting. The Problem is entering the USA back again which will require non-expired VISA.
I don't know if there is any rule where at POE they would allow you to return on the same i-94 without issuing new i-94 in which case you would not need a VISA. A friend of mine travelled to Canada (5-6 years ago) for a week and came back easily w/o a VISA and same i-94.
I don't remember all the details nor I would suggest you to do that unless there is a certain rules that your advisor is aware of.

If you have some time before your travle, I would suggest you to go to Mexico or Canada and get a VISA before traveling. You can get dates online easily in these countries. Many of my friends in those days used to go to Mexcio to extend their visa while they were in Master program and visit Nepal.

Like others said, you cannot travel back on OPT EAD without a valid F1 visa. EAD doesn't allow you to travel to US, only visas or travel permits like Advance Parole do allow to travel back.
Since OPT is associated with F1 status, once you go out of the US, you have to apply for F1 visa with the evidence of your job offer and OPT card. How likely you'll get the visa is another thing. Even though you are legally allowed to get a F1 visa, its all up to the CO and i doubt they will grant you a visa. I suggest you find a way not to travel.

HI,
I do not recommend to travel outside USA with expired F1 visa during OPT. If you have to travel, then you should get F1 VISA renewed in that Country's American Embassy. Do you have all that time to get interview date, appear for an interview ? If not, then risk is all yours.