I can see kinda how this is used to be similar to

'no matter what...'

'mai[f] waa[f] ja[l] ...'

but apparently it can mean 'nevertheless' or 'however' if it used as a 'CONJ' (http://thai2english.com/dictionary/584.html)

Can someone give some examples and use it in a sentence or two to have that meaning?

It's used as an initial clause adverbial just like 'however,' and 'nevertheless' and 'be that as it may' in English. It isn't any more complicated than that - context dictates which translation works best.

These are examples copied and pasted from the 1st and 2nd page of hits I got on Google. Hopefully they illustrate ok how it's used. My translations aren't that great but hopefully suffice to get the point across.

อย่างไรก็ตาม ก็ต้องยอมรับว่าลีกเยอรมันปีนี้ เบรเมนผลงานไปได้ไกลสุดในเวทียุโรป

Whichever way you look at it, you have to agree that in the German league this year, Bremen's performance(results) has been the best in Europe (literally 'has taken them the furthest in the European scene/stage')

อย่างไรก็ตามสิ่งที่เหมือนกันของปฏิกิริยานิวเคลียร์ทั้ง 2 ชนิดนี้ก็คือ เมื่อเกิดการเปลี่ยนแปลงขึ้นในนิวเคลียสแล้ว จะเกิดการปลดปล่อยพลังงานปริมาณมหาศาลออกมา

yàang rai gôr dtaam sìng têe mĕuan gan kŏng bpà-dtì-gì-rí-yaa niw-klia táng 2 chá-nít née gôr keu mêua gèrt gaan bplìan bplaeng kêun nai niw-kliád láew jà gèrt gaan bplòt bplòi palang ngaan bparì-maan má-hăa săan òk maa

Be that as it may, what is similar between these two types of nuclear reactions, is that when there has been a change in the nucleus, an immense quantity of energy will be released.

ทักษิณ อย่างไรก็ตามท่านก็เป็นคนไทย

ták-sĭn yàang rai gôr dtaam tâan gôr bpen kon tai

Thaksin, at the end of the day, is Thai.