You should take oral supplements unless your doctor is recommending injections. If they are recommending injections then I would want to know how often and how much Vitamin D is in an injection. We at the Vitamin D Council promote taking Vitamin D daily and never huge amounts once a month.
It will depend on how much you are going to take as to how long before your levels are better. Did anyone tell you how much to take? For example we recommend 5000iu a day and it will probably take several months to raise your level. If you take more than 5000iu a day then maybe two months. We also promote a reaching a blood level of no less than 50ng/ml to be healthy. Once you reach that level you must continue to supplement or you will go right back to your previous level.
Absolutely it will be beneficial! It equals about 8500iu per day. Taking it once a week is fine. It will probably take a couple of months to get your levels up. I assume they will retest you again or they should. Again you should try and reach at least 50ng/ml. Once you do, you may only need a maintenance dosage of 5000iu per day. This is what most average people need. (So hopefully they will not recommend a lower amount than that.) Let me know if you have anymore questions!