I probably shouldn't go here but......
Michael, Evening Divine Liturgies are an "Antiochian thing" that are to be used on the eve of weekday feast days. Traditionally, the Evening Divine Liturgy, better known as the Vesperal Liturgy, are held up to 4 times per year. That of St. Basil for Holy Thursday and Holy Saturday. That of St. John on Christmas Eve, the eve of the Theophany and on the feast of the Annunciation (if these feasts fall on a Tuesday to Saturday and for the Annunciation may follow even more complicated rules)
Evening Divine Liturgies, other than those indicated above in the Typikon, are an "innovation."
1) So, why are they around?
They were created by the Antiochians (and adopted by some parishes in other jurisdictions) because in our non-Orthodox American (and Canadian culture) we don't have time off nor inclinations to go to these morning services. So, instead of having services attended by one a handful of persons (at best) or, as normally occurred, were not held at all, these services were transferred to the eve (because the liturgical day starts at vespers) so that, not only were the services held, but people could and (ideally) do attend them.
2) Are these Evening Divine Liturgies "wrong"?
Well, yes and no. Based upon the most Typikons (every autocephaleous Church has their own Typikon) yes. However, no parish in any jurisdiction ever follows their typikon 100% correctly. No, because if we hold Liturgies without people attending them, they are no longer liturgies (work of the people) but Catholic masses!
In many "traditionalist jurisdictions" there is some playing with the services. For example, in Israel and Palestine, where some small parishes share one priest, the Sunday Liturgy is served on Friday (the Islamic day off), Saturday and/or Sunday night (after work, because Sunday is a work day in Muslim and Jewish countries).In the Gulf states, "Sunday services" are routinely held on Friday because that is the only day off to pray!
3) Is there an alternative to the Evening Divine Liturgy?
Sure there is. On some feasts, a Vigil is allowed ( a vigil consists of Vespers, Orthros and the Divine Liturgy in the Greek tradition). Some parishes will only have the Divine Liturgy the evening before. Some will have Orthros and then the Divine Liturgy. Others have really early Divine Liturgies (like 6am)
Until recently, the Antiochians were adamant that the weekday services where held as Evening Divine Liturgies. Currently, it appears that there is a greater flexibility on this issue. The important point being that the services are held, whether that evening before or the day of. This issues has been debated to a great deal on several Orthodox sites.To me, whether I like them or not, at least the services are being celebrated.
I hope this helps out.