Strange as it might sound => Though it might sound strange. Try as he might, he wouldn't be accepted to there => However/Though he might try, he wouldn't be accepted there [by them]. ("to there" seems strange since "there" is an adverb) 동사나 형용사가 as 앞으로 나오고 may/might 같은 불확실성을 나타내는 조동사가 있으면, though나 however/whatever, no matter how/what 등의 양보의 뜻을 가지게 돼요. 그러니까 첫 구절은 "이상하게 들릴지도 모르지만", 두 번째는 "아무리 해 봐야 그 사람은 그곳에 받아들여지지 않을 것이다" 정도가 될 것 같네요.