Can I work with my H4 EAD expiring next week and my I94 expiring 2 weeks later?

Yes, if timely filed extensions.

As a C26 spouse of certain H-1B principal nonimmigrants with an unexpired I-94 showing H-4 nonimmigrant status, you can qualify for an automatic extension of up to 180 days if certain. Applicants who have filed Form I-765, Application for Employment Authorization, qualify for automatic extensions of their expiring employment authorization and/or EADs for up to 180 days if you properly filed Form I-765 for a renewal of their employment authorization and/or EAD before their current EAD expired, and are otherwise eligible for a renewal, which means that your renewal application must be under a category that is eligible for an automatic 180-day extension (which includes C26); and the Category on your current EAD matches the "Class Requested" listed on your Form I-797C Notice of Action. For H-4 dependent spouses, you must have an unexpired Form I-94 indicating H-4 status and this must accompany Form I-797C.