Part 1/2

You asked a very difficult question, one historians still struggle today: quantifying and qualifying the Portuguese presence in the Indian Ocean. For start, let's say the situation changed almost year after year, decade through decade. Portuguese also mostly focused their control in the Western Indian Ocean (Arabian sea) while in the east (bay of Bengal, East Asia) they had only limited official presence (Malacca, Macau..) and close to zero "control"

There is also a difference in the extent of control Portuguese had on spice (and other) trade going to Europe and the one going around Asia

Asia - Europe trade

First let's look over the trade of spices to Europe. In the first few years of the Portuguese arrival, they were in some measure very successful in the complete take over the India-Europe spice trade. They harassed the local traders both near the Red Sea and on the Malabar cost, causing a severe shortage of pepper in Egypt. In around 1503 the Venetian merchants in Egypt found no (or at least not nearly enough) pepper available to buy. Subsequently they did not even send the annual galleys in years 1505, 1506 and few times later.Overall the amount of spice Venetian managed to import through Egypt was several times lower then previously. This was very much a result of the active implementation of the early Portuguese policy, formed by Manuel I, explained in a regimento (instruction) to governor Francisco de Albuquerque in around 1505:

And since it seems to us [D. Manuel] that nothing could be more important for our service than to have a fortress at the mouth of the Red Sea or near it, either inside or outside as seems most convenient, for ift hat is sealed then no more spices can pass through to the lands of the [Mamluk] Sultan (Soldam), and everyone in India would give up the fantasy of being able to trade with anyone save us, and also because it is close to the lands of Prester John, from which it seems to us that there could follow great profits for us, firstly in terms of the Christians there, and then a great increase in our treasury, and then in war whenever we want to make it

Instruction above also shows the line of thinking of the Manuel, of his double desire to control all of India trade, and to weaken Mamluks (Manuel had some ideas of using this commercial and military pressure to make Mamluks give up Jerusalem) However the Portuguese could not really continually enforce this blockade of the Red Sea. (Nor could they deal with the subsequent adaptation of local merchants in their effort to avoid the blockade. Nor was the idea that the Red Sea trade was crucial for India actually true)
Red sea being away from Portuguese early footholds in East Africa and India, Portuguese set up a fort on island of Socotra in an attempt to use it as a base to harass the Red Sea in 1507. The island proved to be a bad location, with not enough food or water, and a generally bad position to use to block Red Sea, Portuguese abandoned it in 1511. Albaquerque tried and failed to take Aden or a better port near or in Red Sea in 1513, and the subsequent governors gave up on attempts to do so, citing lack of manpower. Lopo Soares de Albergaria to whom Aden actually surrendered in 1517 but he deemed while he could take it, he couldn't hold it. It is worth noting that Portuguese governors were very split on how to use their limited forces. Almeida thought holding Cochin (on Malabar cost) was enough and refused Diu, Albaquerque in contrast conquered many key towns and tried to take few more, Albergaria stopped this expansion and started consolidating what they had.

So, the Red Sea being only occasionally and poorly blockaded by the Portuguese, the spices trade through Egypt picked up again, in fewer volume though. The Portuguese decided to lower the prices of spice back in Europe ( in 1509 they doubled down the price), in an effort to cut the competition with impossible to match prices rather then through blockade, but it seems the Venetians somehow managed to keep up. Later the pressure reduced as pepper prices started rising again because the Portuguese efforts to keep their Asian holdings became more intensive and as a consequence more expensive. Their position in spice trade in Europe was one of them having the key hold of price setting, while the Venetians (and others) were secondary players, but players still

EDIT after 8 days, and because the comment was gilded (thank you): I finally managed to track down the article which I wanted to quote to illustrate this point exactly. It is "The Changing Pattern of Europe's Pepper and Spice Imports, ca 1400-1700" by C.H.H. Wake available in full here

The quote, from conclusion on page 395 is as follows:

For the greater part of the sixteenth century - up to about 1550 and again in the 1570s and 1580s - the Portuguese accounted for upwards of 75% of Europe's pepper imports and probably as much or more of the spices imported from the East. Even in the mid-century period of Portuguese maritime misadventure, Portugal's pepper and spice imports outweighed those of Mediterranean importers.

and little below:

The Levantine trade was always marginal to the trade of the Portuguese and could flourish only when, and insofar as, Portuguese imports were affected by losses at sea.

wow - such amazing answers. I am no expert but have been doing heaps of research on the East Indies part for a huge boat trip I've put together which follows the Portuguese forts and trading posts from Flores through the Banda islands to Ambon.

The other part of my research is to do with the Portuguese in Ayutthaya (Siam) in the 1500s.

My take on this is they weren't so much pirates though they weren't scared to use a cannon or two if needed be. They were more explorers and traders and were the first Europeans to reach the Spice Islands and set up camp there.

The reason the Portuguese were there first is because France, Spain etc. were basically fighting wars between each other except for Portugal who decided to go sailing instead.

It wasn't long before Europe started taking note of this small kingdom making some serious money on the spice trade. To give you an idea on how big a deal these guys were the pope drew a line down from the Phillipines giving Spain trading rights to everything West and Portugal the rights to everything to the East - see the treaty of tordesillas.

The real pirates in my mind were the Dutch followed closely by the English. The Dutch came in with bigger ships and bigger cannons and basically forced their way in to the East Indies, overtaking the Portuguese forts and trading ports. The English basically did the same to India.

The Dutch eventually took over the spice and sandalwood trade in Indonesia, relegating the Portuguese to Timor.

Anyhow, the Portuguese were no angels but thanks to their caravels and the adoption of the Arabic lateen sails, they had small agile boats that could sail into the wind and became great explorers.

Interestingly one of the things they left behind in many of these places is their religion - areas around the Portuguese settlement in Ayutthaya Thailand are Christian to this day as are places in Flores, Solor etc. in Indonesia.