What word did Jesus use for God in Aramaic? What is the word and pronunciation for God in Aramaic? I saw 'AaLaH'  is the pronunciation for God from this link: Aramaic Lexicon and Concordance  . Did Jesus uses the word 'AaLaH'  for God during his speeches? And also in Aramaic Bible, is this word is used for God?

If this is true then the Arabic word 'Allahu' and this word 'AaLaH' are same or different?

Also I want to know on which language did Jesus cry this expression - "Eloi, Eloi, lama sabachthani"
The normal generic word for God is "alaha"/"aloho" (ܐܠܗܐ), which is linguistically related to the Hebrew word for God "elohim".

The translation of the tetragrammaton, YHWH, on the other hand, is "maria"/"morio" (ܡܪܝܐ), usually decomposed as mar-yah, Lord-Yah ("mar", lord, also being used by syriac speaking churches as a title for saints/doctors of the Church: "mor Ephrem" = Saint Ephrem). (Note: this word has nothing to do with the proper name Maria, coming from the Hebrew Mariam)

To answer your question, Jesus would almost certainly have used one of the two, or both at the same time as it is commonly done in Syriac: Maria Alaha. 

Last remark: The arabic word Allah, used also by Arabic Christians, is no more no less related to the Aramaic Alaha than to the Hebrew Elohim. The three share a common linguistic root, which is nothing exceptional, so no point being dragged on sterile arguments concerning this point.

Concerning the cry on the cross (quote from Psalm 22:1), the Peshitta (the earliest christian Aramaic translation) translate it using the word alaha, with the first person possessive suffix -i : alahi (ܐܲܠܵܗܝ ܐܲܠܵܗܝ ܠܡܵܢܵܐ ܫܒܲܩ̣ܬܵܢܝ̱ ). The original Hebrew Psalm used "Eli". Since the scriptor of the Greek gospel may not have been fluent in Aramaic, or used to transliterate Aramaic with Greek characters, it may be expected that the transliterations are approximates, hence a possible : eloi/alohi confusion.