How can I travel with my EB-5 I-90 and I-797 both expired?

Best to get a temporary green card stamp in your passport before traveling abroad.

The I-90 receipt should give you extended evidence of your permanent residency status. If not, do an INFOPASS for an I-551 stamp in your passport to travel.

It is not clear from the facts whether you have applied to renew your 10-year green card (by filing Form I-90) or whether you had a 2-year conditional green card expired and filed Form I-90 instead of filing for removal of conditions (Form I-829). If the first scenario applies, you can get an I-551 stamp in 1-year increments in a valid foreign passport at your local USCIS office while the case is pending and this allows you to travel and work. If the latter scenario applies, contact an experienced immigration lawyer to assist you further.

The airline will refuse you to board. You can try to apply for a Canada visa and enter Canada first.

Why did you file I-90? Do you possess a conditional permanent resident card (conditional residency) or a permanent resident card (10-year validity)? If you have a 10-year green card and it is expired, you need to file I-90 to "renew" the green card. During the pendency, you can go to a local USCIS to get an I-551 stamp on your passport for travel. If you have fulfilled your conditional residency period, you need to submit I-829 petition to remove the conditions.