This front half of the sentence is saying that the "工程" is completed or progresses in stages (sections) and also has a final deadline. A literal understanding would be the 工程 is completed (进度) is divided (分) into stages (期) or sections (区).

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Note added at 47 mins (2011-07-12 23:19:05 GMT)
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I am sorry, please let me add some information to my answer: the "工程" is completed in stages and while not expressly mentioned here, these stages also have deadlines. This means that there are incremental deadlines as well as a final deadline.

本工程订有分期（区）进度及最后竣工期限或分期（区）完工使用或移交者。
指的应该是：
本工程订有
A. 分期（区）进度及最后竣工期限
B. 或分期（区）完工使用或移交者。

故整句是：
Where stipulated (or prescribed) in this Project with progresses of stages (zones) and final completion deadline or to be used or transferred on completion of stages (zones).

分期，除了by stages 也有习惯用 by phases 或by terms的。这里的分期指的是工程期限的分期，与「分期付款installments」的分期意义不同。
分区，除了by zones，也有习惯用 by phases 或by sections的。分区，这个中文，也有招标文件称之为「分段」（两岸繁简都一样）。

供参考，请参见两岸各类招标文件有官方中英版者（通常没有电子文件，only hard copies）。