I'm looking to quit my job, without notice, in the next few days. Currently the company owes me about $1,500 in travel/business expenses from to business trips I recently took. The company normally takes 45 days to reimburse their employees for expenses. Once I quit, how long do they have to reimburse me and to provide me with my final paycheck?

Your final paycheck, 72 hours if you don't give at least that much notice, or your last day of work if you do give at least 72 hours' notice.

Regarding your expenses, my understanding is that those do not fall under the same time frame as your paycheck because, theoretically, they aren't "wages". Barry?

From the CA-DLSE ENFORCEMENT POLICIES AND INTERPRETATIONS MANUAL:

4.3 Wages Due Quitting Employee.
As discussed at Section 3.4 of this Manual, wages due most employees who quit are due within 72 hours after resignation unless 72 hours previous notice was given. Under most circumstances a quitting employee must return to the office or agency of the employer in the county where the work was performed for his or her wages. (See Section 7.4 of this Manual)

4.3.4 Any Wages.
“Any wages” includes any amount due as wages (see Labor Code § 200, see also, DIR, DLSE v. UI Video, 55 Cal.App.4th 1084, 1091); but does not include expenses. (Hagin v. P ac. Gas & Elec. 152 Cal.App.2d 93)

So based upon this information provided wages are due within 72 hours, reimbursements will be paid but will follow my companies traditional pay out timeline.

That's reading it correctly. Thanks, DAW.