Lets take the two parts separately ...
Housing Loan Principal
Exemption can be claimed under Section 80C and exemption is limited to Rs 1 Lakh for all deductions under this section.
Common knowledge suggests that deduction for housing principal payment can be claimed only after construction is completed.
However to be double sure I checked the actual wording of the relevant section 80C(2) (xviii) of the IT Act. The section is reproduced verbatim below (Empahis added by me)
(xviii) for the purposes of purchase or construction of a residential house property the income from which is chargeable to tax under the head “Income from house property” (or which would, if it had not been used for the assessee’s own residence, have been chargeable to tax under that head), where such payments are made towards or by way of—
(a) any instalment or part payment of the amount due under any self-financing or other scheme of any development authority, housing board or other authority engaged in the construction and sale of house property on ownership basis; or
(b) any instalment or part payment of the amount due to any company or co-operative society of which the assessee is a shareholder or member towards the cost of the house property allotted to him; or
(c) repayment of the amount borrowed by the assessee from—
(1) the Central Government or any State Government, or
(2) any bank, including a co-operative bank, or
(3) the Life Insurance Corporation, or
(4) the National Housing Bank, or
(5) any public company formed and registered in India with the main object of carrying on the business of providing long-term finance for construction or purchase of houses in India for residential purposes which is eligible for deduction under clause (viii) of sub-section (1) of section 36, or
(6) any company in which the public are substantially interested or any co-operative society, where such company or co-operative society is engaged in the business of financing the construction of houses, or
(7) the assessee’s employer where such employer is an authority or a board or a corporation or any other body established or constituted under a Central or State Act, or
(8) the assessee’s employer where such employer is a public company or a public sector company or a university established by law or a college affiliated to such university or a local authority or a co-operative society; or
(d) stamp duty, registration fee and other expenses for the purpose of transfer of such house property to the assessee,
but shall not include any payment towards or by way of—
(A) the admission fee, cost of share and initial deposit which a shareholder of a company or a member of a co-operative society has to pay for becoming such shareholder or member; or
(B) the cost of any addition or alteration to, or renovation or repair of, the house property which is carried out after the issue of the completion certificate in respect of the house property by the authority competent to issue such certificate or after the house property or any part thereof has either been occupied by the assessee or any other person on his behalf or been let out; or
(C) any expenditure in respect of which deduction is allowable under the provisions of section 24;
You should note that there is nothing in the section that excludes property under construction.
Housing Loan Interest
Exemption can be claimed under Section 24.
If loan was taken prior to 1st April 1999, interest payment up to Rs 30,000 can be deducted. For loan taken on or after 1st April 1999 interest payment up to Rs 1,50,000 can be deducted.
If loan installments are paid before construction is completed and possession is taken, then the interest paid for the 5 years prior to the year when construction is completed and possesion is taken can be claimed in equal installments over the next 5 years.
However the total interest deduction claimed is subject to Rs 1,50,000 limit irrespective of the fact that interest for period prior to completion of construction is claimed.
Please note that these are my opinions after reading the relevant sections of the IT Act. I am not a tax or legal expert and my interpretation may be wrong. Please consult an appropriate professional expert for confirmation.