Taken on its own, "after work" can be translated into "เลิกงาน", "งานเลิก", "หลังเลิกงาน", "หลังงานเลิก", "งานเสร็จ", "เสร็จงาน", etc. It is not wrong to translate it directly into "หลังงานเลิก", a Thai person from southern Thailand like Toongsong or Nakorn Sri Thammarat would probably say it that way. With my humble experience, I would translate your sentence this way:

เลิกงานวันนี้อยากไปดื่มเหล้ากับผม(ฉัน)สักแก้วไหม?

Literary back translation:
"After work today would you like to join me (with the female form in bracket) to drink a glass of alcoholic drink?"

Note the addition of "today" in the target text. Note the placing of the time phrase, "after work today", at the front of the sentence. Note the meaning of a "drink" in English, particularly when "a drink" is mentioned. Some Thais do not know that it is supposed to be an "alcoholic" drink. Note also the addition of "a glass of" to take into consideration your article "a".