I've offered to do the job in exchange for a week's accommodation.

用现在完成时很正常。表示 offer 这个动作在过去已经发生，总不能是经常习惯性动作吧？要么，使用一般过去时，也可以。

in exchange for  是个“短语介词”。意思是“为了换取”。类似结构的表达有：

in favor of  有利于…… 

in fear of  害怕

in front of  在……前面

in honor of 为了纪念……     

in memory of 为了纪念……

in need of  需要      

in place of 代替

in search of 寻找

I've offered to do the job in exchange for a week's accommodation.

【翻译】我提出做这项工作以换取一周的住宿。