Do be sure to look closely at the rules for accruing miles from EVA Air onto Continental --
http://www.continental.com/CMS/en-US...aspx?ItemId=71.
Note that you'll only earn miles for fares in the Y or K booking classes. (The cheapest EVA flight I see on a random weekend in February is in the K booking class, so you should probably be OK -- but you might want to double-check before you buy.)
In general, go to "Earn Miles" -> "Airline Partners" on both united.com and continental.com to see the mileage accrual rules.
Of course since they're not a Star Alliance member you'll only earn redeemable miles (for free trips!), not elite qualifying miles (for frequent flyer status).